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Keywords: covariance matrix
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Journal Articles
Journal: SPE Journal
SPE J. (2022)
Paper Number: SPE-210084-PA
Published: 21 September 2022
... at the horizontal east/west tangent sections. Copyright © 2022 Society of Petroleum Engineers measurement while drilling drilling measurement information jacobian matrix covariance matrix matrix msa correction upstream oil & gas drilling data acquisition vector accuracy drillstring design...
Includes: Supplementary Content
Journal Articles
Journal: SPE Journal
SPE J. 27 (04): 2510–2524.
Paper Number: SPE-209585-PA
Published: 11 August 2022
... forecasts which promote a wide ensemble spread of forecast realizations. Static parameters are assumed to be constant over time; however, they can be augmented to the state variable to update both model state and parameters. Using these forecast ensembles, the ensemble forecast covariance matrix, C...
Journal Articles
Journal: SPE Journal
SPE J. (2022)
Paper Number: SPE-210563-PA
Published: 08 July 2022
... reservoir characterization surface relaxivity vector-valued gp decay machine learning objective function relaxation time hyperparameter optimization problem log analysis null 2 null 1 null sim covariance matrix Copyright © 2022 The Authors. Published by the Society of Petroleum Engineers...
Journal Articles
Journal: SPE Journal
SPE J. 25 (06): 3300–3316.
Paper Number: SPE-193838-PA
Published: 17 December 2020
... is similar to the third approach; however, an additional covariance matrix of difference between a PCA‐based error model and the corresponding actual realizations of prior error is added to the covariance matrix of the measurement error. The first newly introduced algorithm (fifth approach) relies...
Journal Articles
Journal: SPE Journal
SPE J. 25 (05): 2162–2177.
Paper Number: SPE-201230-PA
Published: 15 October 2020
... of the topside fluid flow path. drilling fluids and materials flowline artificial intelligence upstream oil & gas well model drilling fluid management & disposal annular pressure drilling fluid loss well control drilling operation flow rate covariance matrix true value topside...
Journal Articles
Journal: SPE Journal
SPE J. 25 (01): 037–055.
Paper Number: SPE-193916-PA
Published: 17 February 2020
... to a synthetic history‐matching problem for demonstration. Artificial Intelligence Upstream Oil & Gas machine learning history matching reservoir simulation objective function covariance matrix history-matching problem error function gmm approximation training data uncertain parameter Bayesian...
Journal Articles
Journal: SPE Journal
SPE J. 21 (02): 501–521.
Paper Number: SPE-173256-PA
Published: 14 April 2016
... matrix. This covariance matrix is used to impose a temporal correlation on the controls at each well. In this approach, well controls are parameterized in terms of a few optimization parameters to reduce the dimension of the joint optimization problem. Moreover, the imposed smoothness on the well...
Journal Articles
Journal: SPE Journal
SPE J. 20 (01): 155–168.
Paper Number: SPE-163657-PA
Published: 09 February 2015
... the gradient of the objective function with respect to the controls. Current implementations of EnOpt use a Gaussian ensemble of control perturbations with a constant covariance matrix, and thus a constant perturbation size, during the entire optimization process. The covariance-matrix-adaptation evolutionary...
Journal Articles
Journal: SPE Journal
SPE J. 18 (06): 1003–1011.
Paper Number: SPE-143292-PA
Published: 17 April 2013
..., which are CPU-time-demanding. This paper presents the use of the CMA-ES (covariance matrix adaptation—evolution strategy) optimizer, recognized as one of the most powerful derivative free optimizers, to optimize well locations and trajectories. A local-regression-based metamodel is incorporated...
Journal Articles
Journal: SPE Journal
SPE J. 17 (01): 307–320.
Paper Number: SPE-134315-PA
Published: 07 November 2011
... 2012 initial reservoir pressure Artificial Intelligence Drillstem Testing pressure data unit-rate drawdown response drillstem/well testing pressure-derivative data deconvolution covariance matrix pressure transient analysis pressure transient testing objective function deconvolved response...
Journal Articles
Journal: SPE Journal
SPE J. 15 (02): 495–508.
Paper Number: SPE-118952-PA
Published: 17 December 2009
... better determined and the variability in the set of reservoir descriptions that provide an acceptable match of production data is reduced. They propose a reduction in the number of parameters by using the eigenvectors of the model covariance matrix to define the new basis. Shah et al. (1978) compared...
Journal Articles
Journal: SPE Journal
SPE J. 14 (03): 393–412.
Paper Number: SPE-117274-PA
Published: 27 September 2009
... by a covariance matrix) and an observation equation that relates a linear combination of the states to measurements. The measurements are also associated with uncertainty. The model equations are used to compute a forward step ( Eqs. 1 and 2 ) where the state variables are computed forward in time...
Journal Articles
Journal: SPE Journal
SPE J. 13 (04): 412–422.
Paper Number: SPE-103268-PA
Published: 15 December 2008
...) method. Efficient implementations of this method require a posterior covariance matrix for layer thicknesses. Under assumptions that are not too restrictive, the inverse of the posterior covariance matrix can be approximated as a Toeplitz matrix, which makes the MCMC calculations efficient. The proposed...
Journal Articles
Journal: SPE Journal
SPE J. 12 (03): 382–391.
Paper Number: SPE-95750-PA
Published: 19 September 2007
... assimilation zafari optimization problem central model bottomhole pressure characterization posterior PDF reservoir characterization vector water cut ensemble Kalman filter covariance matrix Our main interest is in characterizing the uncertainty in reservoir description and reservoir...
Journal Articles
Journal: SPE Journal
SPE J. 12 (03): 282–292.
Paper Number: SPE-95789-PA
Published: 19 September 2007
... permeability ensemble Kalman filter history matching Modeling & Simulation seismic data covariance matrix base case ensemble production data ensemble mean permeability measurement error bergen The Kalman filter was originally developed to update the states of linear systems ( Kalman 1960...
Journal Articles
Journal: SPE Journal
SPE J. 12 (01): 108–117.
Paper Number: SPE-95277-PA
Published: 19 March 2007
... the covariance matrix of state variables, which is computationally expensive for large-scale problems with millions of gridblocks. In the ensemble Kalman filter (EnKF), this problem is alleviated with sampling from a limited number of realizations and computing the required subset of the covariance matrix...
Journal Articles
Journal: SPE Journal
SPE J. 10 (01): 66–74.
Paper Number: SPE-84372-PA
Published: 15 March 2005
... correspond upstream oil & gas ensemble covariance matrix true solution reservoir simulation x-axis correspond reference solution permeability reservoir model saturation flow in porous media history matching state variable fluid dynamics forecast filter solution In the management...
Journal Articles
Journal: SPE Journal
SPE J. 9 (03): 330–338.
Paper Number: SPE-88961-PA
Published: 01 September 2004
..., if we assume that the prior model has a multivariate Gaussian distribution with a covariance matrix C M and the production data has Gaussian uncertainty described by the data covariance C d , then the Bayesian approach leads to the following posterior distribution 6 : (1) P ( m...
Journal Articles
Journal: SPE Journal
SPE J. 9 (01): 67–78.
Paper Number: SPE-87680-PA
Published: 01 March 2004
...) to the case in which the prior covariance matrix is nondiagonal. We show that the parameter selection can be made independently of the weight assigned to the prior information, and illustrate how the shape of the gradzones is modified to reflect the correlation structure of the porosity or permeability fields...
Journal Articles
Journal: SPE Journal
SPE J. 7 (03): 243–249.
Paper Number: SPE-79582-PA
Published: 01 September 2002
.... Although the resulting estimates of model parameters may be reasonable, calculated confidence intervals are meaningless. Here, we show how to compute the correct derivative data covariance matrix that should be used for estimating parameters by nonlinear least squares. It is also shown that the information...

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