Bridging the Gap Between Deterministic and Probabilistic Uncertainty Quantification Using Advanced Proxy Based Methods

Goodwin, Nigel

doi:10.2118/173301-ms

Cited by 48 publications

(18 citation statements)

References 256 publications

(178 reference statements)

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“…In addition, the standard MH algorithm has a lower acceptance ratio [69] than other MCMC algorithms such as delayed rejection [70], adaptive Metropolis [71], and the combination of delayed rejection and adaptive Metropolis [72]. A good summary and discussion of the advanced MCMC algorithms can be found in Goodwin [73]. To improve the MH algorithm, Yu et al [74] proposed a new probabilistic approach with the Bayesian methodology combined with MCMC sampling and a FDC decline curve model to increase the efficiency and reliability of the uncertainty quantification.…”

Section: Probabilistic Decline Curve Modelmentioning

confidence: 99%

Methods of Decline Curve Analysis for Shale Gas Reservoirs

2018

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Abstract:With help from horizontal wells and hydraulic fracturing, shale gas has made a significant contribution to the energy supply. However, due to complex fracture networks and complicated mechanisms such as gas desorption and gas slippage in shale, forecasting shale gas production is a challenging task. Despite the versatility of many simulation methods including analytical models, semi-analytical models, and numerical simulation, Decline Curve Analysis has the advantages of simplicity and efficiency for hydrocarbon production forecasting. In this article, the eight most popular deterministic decline curve methods are reviewed: Arps, Logistic Growth Model, Power Law Exponential Model, Stretched Exponential Model, Duong Model, Extended Exponential Decline Model, and Fractural Decline Curve model. This review article is dedicated to summarizing the origins, derivations, assumptions, and limitations of these eight decline curve models. This review article also describes the current status of decline curve analysis methods, which provides a comprehensive and up-to-date list of Decline Curve Analysis models for petroleum engineers in analysis of shale gas reservoirs. This work could serve as a guideline for petroleum engineers to determine which Decline Curve models should be applied to different shale gas fields and production periods.

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Section: Probabilistic Decline Curve Modelmentioning

confidence: 99%

Methods of Decline Curve Analysis for Shale Gas Reservoirs

2018

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“…Uncertainty quantification using reservoir simulation models is becoming increasingly important for making field development decisions (Subbey et al 2004;Webb et al 2008;Oliver and Chen 2011;Bazargan et al 2013;Goodwin 2015). For brown fields that have been discovered and developed enough to have historical production data, an ensemble of history-matched reservoir models that are constrained by field production data are required in order to quantify the uncertainty of production forecast.…”

Section: Introductionmentioning

confidence: 99%

“…Various optimization algorithms have been applied in reservoir simulation studies, including Genetic Algorithm, Evolution Strategy, Differential Evolution, Particle Swarm Optimization, Gradual Deformation, and Adjoint (Oliver and Chen 2011;Mirzabozorg et al 2013;Goodwin 2015). These algorithms generate a sequence of parameter values that generally improve the history match as more simulations are performed.…”

Section: Introductionmentioning

confidence: 99%

“…These algorithms generate a sequence of parameter values that generally improve the history match as more simulations are performed. However, because optimization algorithms are not designed for uncertainty quantification, the set of simulation runs created by an optimization algorithm can be biased and does not necessarily characterize the probabilistic distribution even if some post-processing schemes such as de-clustering or weighting are applied (Bazargan et al 2013;Goodwin 2015). To examine the impact of algorithm choices on forecast uncertainty, Erbas and Christie (2007) used a North Sea field example to show that the choice of optimization algorithm and algorithm settings significantly affect the forecast uncertainty.…”

Section: Introductionmentioning

confidence: 99%

“…As a result, a sufficiently large number of MCMC samples are required to avoid potential bias and to correctly characterize the posterior pdf. Recently, the Hamiltonian Monte Carlo method has been applied in uncertainty quantification of reservoir simulation models (Goodwin 2015). It differs from the Metropolis-Hastings algorithm by reducing the correlation between successive samples to improve the convergence.…”

Section: Introductionmentioning

confidence: 99%

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An Efficient and Practical Workflow for Probabilistic Forecasting of Brown Fields Constrained by Historical Data

Yang¹,

Nghiem²,

Erdle³

et al. 2015

SPE Annual Technical Conference and Exhibition

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Brown fields are fields with significant production history. Probabilistic forecasting for brown fields requires multiple history-matched models that are conditioned to available field production data. This paper presents a systematic and practical workflow to generate an ensemble of simulation models that is able to capture uncertainties in forecasts, while honoring the observed production data.The proposed workflow employs the Bayes theorem to define a posterior Probability Density Function (PDF) that represents model forecast uncertainty by incorporating the misfit between simulation results and measured production data. Previous workflows use the Markov Chain Monte Carlo (MCMC) sampling method, which requires an extremely large number (thousands) of simulation runs. To alleviate this drawback, a Proxy-based Acceptance-Rejection (PAR) sampling method is developed in this study to generate representative simulation models that characterize the posterior PDF using hundreds of simulation runs. The proposed workflow can be summarized in five key steps:1. Run an initial set of reservoir simulations by simultaneously varying multiple uncertain parameters using an experimental design method. 2. Construct a proxy function using a Radial-Basis Function (RBF) neural network to approximate the posterior PDF calculated from the initial set of simulation results. 3. Sample the posterior PDF using the PAR sampling method and run an ensemble of new simulation models using the sample values. 4. The new simulation results obtained in step 3 are added to the training datasets generated in step 1 to improve the accuracy of the proxy function. Steps 3 and 4 are repeated until a predefined stop criterion is satisfied. 5. Filter all simulation runs generated in step 3 using appropriate tolerance criteria for various history-match quality indicators. The selected filtered cases constitute the final ensemble of simulation models that can be further used for uncertainty quantification in forecasting.The proposed workflow is demonstrated on two reservoir simulation models:1. Synthetic case. The forecast uncertainty of the ninth SPE Comparative Solution Project (SPE9) simulation model is investigated with a synthetic production history and 32 uncertain parameters. 2. Unconventional oil field case. The workflow is applied to an Eagle Ford shale oil well to determine P90 (conservative), P50 (most likely), and P10 (optimistic) cases of estimated ultimate recovery (EUR).Results of the workflow are compared to those obtained using the Metropolis-Hasting MCMC sampling method. The comparison shows that the proposed workflow only requires 800 simulation runs to obtain results as accurate as the MCMC method with 8000 simulation runs. This translates into a 10times speedup, which makes the proposed workflow practical for many real reservoir simulation studies.

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Rapid evaluation and optimization of carbon dioxide‐enhanced oil recovery using reduced‐physics proxy models

Al‐Mudhafar

Rao

Srinivasan

et al. 2022

Energy Science & Engineering

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The carbon dioxide (CO2) injection in oil reservoirs is a promising enhanced oil recovery method to reduce carbon emissions into the atmosphere. The CO2 injection simulation and optimization require a large computation time, especially in real large‐scale oil reservoirs. This paper integrates experimental design and machine learning to construct a reduced‐physics surrogate model alternative to the complex reservoir simulator. This surrogate model was used to evaluate and optimize the CO2‐assisted gravity drainage (CO2‐GAGD) process, applied to a clastic reservoir in the Rumaila oil field. In the GAGD process optimization, five operational decision parameters controlling the production and injection activities were manipulated to attain optimal future oil production. Hundreds of simulation runs were created by Latin Hypercube Sampling to build a proxy‐based optimization. The optimal scenario increased the cumulative oil production by 416 MMSTB at the end of 10‐year prediction period. Finally, four machine learning (ML) algorithms were built as proxy surrogates alternative to the complex compositional reservoir simulations: Quadratic Equation (QM), FUzzy logic‐GEnetic algorithm (FUzzy‐GEnetic), Multivariate Additive Regression Splines (MARS), and Generalized Boosted Modeling (GBM). To show how robust using the ML approaches for the fast CO2‐GAGD process optimization, the random subsampling cross‐validation was adopted to conclude the optimum proxy metamodel that provides the lowest mismatch between the proxy‐ and simulator‐based cumulative oil production. The GBM algorithm achieved the highest adjusted‐R2 (0.9973) and lowest root mean square prediction error MathClass-open( 3.704 × 1 0 6 MathClass-close) $(3.704\times 1{0}^{6})$ to produce the most accurate metamodel. The resulting accurate GBM proxy metamodel can be used for fast optimization of the CO2‐GAGD process. Specifically, GBM‐metamodel should lead to achieving higher optimal reservoir flow responses, especially with running a large number of simulation runs. Consequently, this proposed trained GBM‐ML proxy metamodel could be used for gas injection optimization and uncertainty assessment with far‐less computational effort than with the conventional approaches, which use a complex flow simulator.

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Bridging the Gap Between Deterministic and Probabilistic Uncertainty Quantification Using Advanced Proxy Based Methods

Cited by 48 publications

References 256 publications

Methods of Decline Curve Analysis for Shale Gas Reservoirs

Methods of Decline Curve Analysis for Shale Gas Reservoirs

An Efficient and Practical Workflow for Probabilistic Forecasting of Brown Fields Constrained by Historical Data

Rapid evaluation and optimization of carbon dioxide‐enhanced oil recovery using reduced‐physics proxy models

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