Comparison of Evolutionary and Swarm Intelligence Methods for History Matching and Uncertainty Quantification in Petroleum Reservoir Models

2011 ◽  
pp. 209-240 ◽  
Author(s):  
Yasin Hajizadeh ◽  
Vasily Demyanov ◽  
Linah Mohamed ◽  
Mike Christie
Keyword(s):  
Uncertainty Quantification ◽  
Swarm Intelligence ◽  
History Matching ◽  
Petroleum Reservoir ◽  
Reservoir Models

Comparison of Stochastic Sampling Algorithms for Uncertainty Quantification

SPE Journal ◽  
2009 ◽  
Vol 15 (01) ◽  
pp. 31-38 ◽  
Author(s):  
Linah Mohamed ◽  
Mike Christie ◽  
Vasily Demyanov
Keyword(s):  
Monte Carlo ◽  
Uncertainty Quantification ◽  
Swarm Intelligence ◽  
Parameter Space ◽  
History Matching ◽  
Hamiltonian Dynamics ◽  
Gradient Methods ◽  
Stochastic Sampling ◽  
Reservoir Models ◽  
Sampling Algorithms

Summary History matching and uncertainty quantification are two important research topics in reservoir simulation currently. In the Bayesian approach, we start with prior information about a reservoir (e.g., from analog outcrop data) and update our reservoir models with observations (e.g., from production data or time-lapse seismic). The goal of this activity is often to generate multiple models that match the history and use the models to quantify uncertainties in predictions of reservoir performance. A critical aspect of generating multiple history-matched models is the sampling algorithm used to generate the models. Algorithms that have been studied include gradient methods, genetic algorithms, and the ensemble Kalman filter (EnKF). This paper investigates the efficiency of three stochastic sampling algorithms: Hamiltonian Monte Carlo (HMC) algorithm, Particle Swarm Optimization (PSO) algorithm, and the Neighbourhood Algorithm (NA). HMC is a Markov chain Monte Carlo (MCMC) technique that uses Hamiltonian dynamics to achieve larger jumps than are possible with other MCMC techniques. PSO is a swarm intelligence algorithm that uses similar dynamics to HMC to guide the search but incorporates acceleration and damping parameters to provide rapid convergence to possible multiple minima. NA is a sampling technique that uses the properties of Voronoi cells in high dimensions to achieve multiple history-matched models. The algorithms are compared by generating multiple history- matched reservoir models and comparing the Bayesian credible intervals (p10-p50-p90) produced by each algorithm. We show that all the algorithms are able to find equivalent match qualities for this example but that some algorithms are able to find good fitting models quickly, whereas others are able to find a more diverse set of models in parameter space. The effects of the different sampling of model parameter space are compared in terms of the p10-p50-p90 uncertainty envelopes in forecast oil rate. These results show that algorithms based on Hamiltonian dynamics and swarm intelligence concepts have the potential to be effective tools in uncertainty quantification in the oil industry.

Numerical Comparison Between ES-MDA and Gradient-Based Optimization for History Matching of Reduced Reservoir Models

2021 ◽  
Author(s):  
M. A. Borregales Reverón ◽  
H. H. Holm ◽  
O. Møyner ◽  
S. Krogstad ◽  
K.-A. Lie
Keyword(s):  
History Matching ◽  
Automatic Differentiation ◽  
Computational Cost ◽  
Numerical Comparison ◽  
Petroleum Reservoir ◽  
History Match ◽  
Reservoir Models ◽  
Multiple Data ◽  
Future Production ◽  
Gradient Based

Abstract The Ensemble Smoother with Multiple Data Assimilation (ES-MDA) method has been popular for petroleum reservoir history matching. However, the increasing inclusion of automatic differentiation in reservoir models opens the possibility to history-match models using gradient-based optimization. Here, we discuss, study, and compare ES-MDA and a gradient-based optimization for history-matching waterflooding models. We apply these two methods to history match reduced GPSNet-type models. To study the methods, we use an implementation of ES-MDA and a gradient-based optimization in the open-source MATLAB Reservoir Simulation Toolbox (MRST), and compare the methods in terms of history-matching quality and computational efficiency. We show complementary advantages of both ES-MDA and gradient-based optimization. ES-MDA is suitable when an exact gradient is not available and provides a satisfactory forecast of future production that often envelops the reference history data. On the other hand, gradient-based optimization is efficient if the exact gradient is available, as it then requires a low number of model evaluations. If the exact gradient is not available, using an approximate gradient or ES-MDA are good alternatives and give equivalent results in terms of computational cost and quality predictions.

Uncertainty Quantification Using Streamline Based Inversion and Distance Based Clustering

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Jihoon Park ◽  
Jeongwoo Jin ◽  
Jonggeun Choe
Keyword(s):  
Uncertainty Quantification ◽  
Travel Time ◽  
History Matching ◽  
Reservoir Characterization ◽  
Uncertainty Assessment ◽  
Dynamic Responses ◽  
Time Inversion ◽  
Dynamic Data ◽  
Reservoir Models ◽  
Permeability Distribution

For decision making, it is crucial to have proper reservoir characterization and uncertainty assessment of reservoir performances. Since initial models constructed with limited data have high uncertainty, it is essential to integrate both static and dynamic data for reliable future predictions. Uncertainty quantification is computationally demanding because it requires a lot of iterative forward simulations and optimizations in a single history matching, and multiple realizations of reservoir models should be computed. In this paper, a methodology is proposed to rapidly quantify uncertainties by combining streamline-based inversion and distance-based clustering. A distance between each reservoir model is defined as the norm of differences of generalized travel time (GTT) vectors. Then, reservoir models are grouped according to the distances and representative models are selected from each group. Inversions are performed on the representative models instead of using all models. We use generalized travel time inversion (GTTI) for the integration of dynamic data to overcome high nonlinearity and take advantage of computational efficiency. It is verified that the proposed method gathers models with both similar dynamic responses and permeability distribution. It also assesses the uncertainty of reservoir performances reliably, while reducing the amount of calculations significantly by using the representative models.

scholarly journals History matching of petroleum reservoir models by the Ensemble Kalman Filter and parameterization methods

2013 ◽  
Vol 55 ◽  
pp. 84-95 ◽  
Author(s):  
Leila Heidari ◽  
Véronique Gervais ◽  
Mickaële Le Ravalec ◽  
Hans Wackernagel
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Petroleum Reservoir ◽  
Reservoir Models

Bayesian Optimization Algorithm Applied to Uncertainty Quantification

SPE Journal ◽  
2012 ◽  
Vol 17 (03) ◽  
pp. 865-873 ◽  
Author(s):  
Asaad Abdollahzadeh ◽  
Alan Reynolds ◽  
Mike Christie ◽  
David Corne ◽  
Brian Davies ◽  
...  
Keyword(s):  
Uncertainty Quantification ◽  
Optimization Algorithm ◽  
History Matching ◽  
Search Space ◽  
Population Based ◽  
Optimization Techniques ◽  
Bayesian Optimization ◽  
Similar Response ◽  
Bayesian Optimization Algorithm ◽  
Reservoir Models

Summary Prudent decision making in subsurface assets requires reservoir uncertainty quantification. In a typical uncertainty-quantification study, reservoir models must be updated using the observed response from the reservoir by a process known as history matching. This involves solving an inverse problem, finding reservoir models that produce, under simulation, a similar response to that of the real reservoir. However, this requires multiple expensive multiphase-flow simulations. Thus, uncertainty-quantification studies employ optimization techniques to find acceptable models to be used in prediction. Different optimization algorithms and search strategies are presented in the literature, but they are generally unsatisfactory because of slow convergence to the optimal regions of the global search space, and, more importantly, failure in finding multiple acceptable reservoir models. In this context, a new approach is offered by estimation-of-distribution algorithms (EDAs). EDAs are population-based algorithms that use models to estimate the probability distribution of promising solutions and then generate new candidate solutions. This paper explores the application of EDAs, including univariate and multivariate models. We discuss two histogram-based univariate models and one multivariate model, the Bayesian optimization algorithm (BOA), which employs Bayesian networks for modeling. By considering possible interactions between variables and exploiting explicitly stored knowledge of such interactions, EDAs can accelerate the search process while preserving search diversity. Unlike most existing approaches applied to uncertainty quantification, the Bayesian network allows the BOA to build solutions using flexible rules learned from the models obtained, rather than fixed rules, leading to better solutions and improved convergence. The BOA is naturally suited to finding good solutions in complex high-dimensional spaces, such as those typical in reservoir-uncertainty quantification. We demonstrate the effectiveness of EDA by applying the well-known synthetic PUNQ-S3 case with multiple wells. This allows us to verify the methodology in a well-controlled case. Results show better estimation of uncertainty when compared with some other traditional population-based algorithms.

History matching reservoir models simulated from the pluri-Gaussian method

2005 ◽  
Author(s):  
Paul Thomas ◽  
Mickaele Le Ravalec-Dupin ◽  
Frederic Roggero
Keyword(s):  
History Matching ◽  
Reservoir Models ◽  
Gaussian Method
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