An analysis of history matching errors

Tavassoli, Z.; Carter, Jonathan N.; King, Peter R.

doi:10.1007/s10596-005-9001-7

Cited by 29 publications

(18 citation statements)

References 36 publications

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“…To show that the results obtained in this paper are more generic, we have carried out a further study in Ref. 56, which investigates the errors both in history matching and in prediction by systematically varying each parameter in the reservoir model.…”

Section: Discussionmentioning

confidence: 99%

Errors in History Matching

2004

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The usual procedure in history matching is to adopt a Bayesian approach with an objective function that is assumed to have a single simple minimum at the "correct" model. In this paper, we use a simple cross-sectional model of a reservoir to show that this may not be the case. The model has three unknown parameters: high and low permeabilities and the throw of a fault. We generate a large number of realizations of the reservoir and choose one of them as a base case. Using the weighted sum of squares for the objective function, we find both the best production-and best parameter-matched models. The results show that a good fit for the production data does not necessarily have a good estimation for the parameters of the reservoir, and therefore it may lead to a bad forecast for the performance of the reservoir. We discuss the idea that the "true" model (represented here by the base case) is not necessarily the most likely to be obtained using conventional history-matching methods. Reservoir Model and Objective FunctionWe use a simple 2D cross-sectional model of a layered reservoir, as shown in Fig. 1. 57 The model is 2D, with no-flow boundary conditions. Water is injected on the left side, and a production well is located on the right. There is a single, normal fault at the midpoint between the two wells. The reservoir contains six alternating layers of good-and poor-quality sands with high and low permeabilities, respectively. The porosities of the good-and poor-quality sands are 0.30 and 0.15, respectively. We also assume that the three good-quality layers have identical properties, and the three poor-quality layers have a different set of identical properties. The thickness of the layers has an arithmetic progression, with the top layer having a thickness of 12.5 ft, the bottom layer a thickness of 7.5 ft, and with a total thickness of 60 ft. The width of the model

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Section: Discussionmentioning

confidence: 99%

Errors in History Matching

2004

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“…In another example with a highly irregular objective function, Tavassoli et al [163] investigated a twodimensional cross-sectional layered reservoir that was characterized by three parameters: fault throw, permeability of the good and the poor sands. The objective function was analyzed for cases in which two of the three variables were fixed, while the other was varied.…”

Section: Shape Of the Objective Functionmentioning

confidence: 99%

Recent progress on reservoir history matching: a review

2010

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History matching is a type of inverse problem in which observed reservoir behavior is used to estimate reservoir model variables that caused the behavior. Obtaining even a single history-matched reservoir model requires a substantial amount of effort, but the past decade has seen remarkable progress in the ability to generate reservoir simulation models that match large amounts of production data. Progress can be partially attributed to an increase in computational power, but the widespread adoption of geostatistics and Monte Carlo methods has also contributed indirectly. In this review paper, we will summarize key developments in history matching and then review many of the accomplishments of the past decade, including developments in reparameterization of the model variables, methods for computation of the sensitivity coefficients, and methods for quantifying uncertainty. An attempt has been made to compare representative procedures and to identify possible limitations of each.

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“…The ICF test case was first published by Tavassoli et al (2004Tavassoli et al ( , 2005 as a simple yet challenging example of history matching in petroleum engineering applications. Since then, ICF has proved a difficult test for optimization techniques due to numerous local minima.…”

Section: The Imperial College Fault (Icf) Test Casementioning

confidence: 99%

“…Many optimizations and inference techniques have been applied to the ICF problem over the years. The first studies of this test case (Tavassoli et al, 2004(Tavassoli et al, , 2005Carter et al, 2006) have employed a pure Monte Carlo approach, which required nearly 160'000 samples of the parameter space. Christie et al (2006) demonstrated that a good representation of the uncertainty can be inferred from a few thousand samples using…”

Section: The Imperial College Fault (Icf) Test Casementioning

confidence: 99%

Accelerating Monte Carlo Markov chains with proxy and error models

Josset

Demyanov

Elsheikh

et al. 2015

Computers & Geosciences

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In groundwater modeling, Monte Carlo Markov Chain (MCMC) simulations are often used to calibrate aquifer parameters and propagate the uncertainty to the quantity of interest (e.g., pollutant concentration). However, this approach requires a large number of flow simulations and incurs high computational cost, which prevents a systematic evaluation of the uncertainty in presence of complex physical processes. To avoid this computational bottleneck, we propose to use an approximate model (proxy) to predict the response of the exact model. Here, we use a proxy that entails a very simplified description of the physics with respect to the detailed physics described by the "exact" model. The error model accounts for the simplification of the physical process; and it is trained on a learning set of realizations, for which both the proxy and exact responses are computed. First, the key features of the set of curves are extracted using functional principal component analysis; then, a regression model is built to characterize the relationship between the curves. The performance of the proposed approach is evaluated on the Imperial College Fault model. We show that the joint use of the proxy and the error model to infer the model parameters in a two-stage MCMC setup allows longer chains at a comparable computational cost. Unnecessary evaluations of the exact responses are avoided through a preliminary evaluation of the proposal made on the basis of the corrected proxy response. The error model trained on the learning set is crucial to provide a sufficiently accurate prediction of the exact response and guide the chains to the low misfit regions. The proposed methodology can be extended to multiple-chain algorithms or other Bayesian inference methods. Moreover, FPCA is not limited to the specific presented application and offers a general framework to build error models.

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An analysis of history matching errors

Cited by 29 publications

References 36 publications

Errors in History Matching

Errors in History Matching

Recent progress on reservoir history matching: a review

Accelerating Monte Carlo Markov chains with proxy and error models

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