Gradients Method Constrained by Geological Bodies for History Matching

Rahon, Daniel; Blanc, Georges; Guérillot, Dominique

doi:10.2118/36568-ms

Cited by 18 publications

(9 citation statements)

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“…the parameterization of the fine scale model) . We calculate these sensitivity coefficients aP/ó9; using the gradient method ( [7], [ 8]). Derivation of the flow equations witti respect to B, requires then the knowledge of 2Kl78; , and consequently the derivation of the upscaling, truncation and gradual deformation steps.…”

Section: Principle Of the Methodologymentioning

confidence: 99%

Direct Conditioning of Fine-Scale Facies Models to Dynamic Data by Combining Gradual Deformation and Numerical Upscaling Techniques

Schaaf¹,

Mezghani²,

Chavent³

2002

ECMOR VIII - 8th European Conference on the Mathematics of Oil Recovery

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Updating reservoir models through dynamic data integration requires the solution of an inverse problem that may be computationally intensive for multi-million cells geological models . History matching is commonly performed using upscaled flow simulation models without updating the original fine grid geological model . In this way, the drawback is that the consistency with the geostatistical parameters is no Jonger ensured .In this paper, we present a new methodology to directly update fine scale geostatistically-based facies models by combining the gradual deformation method for the fine scale model parameterization and numerical upscaling techniques for the coarse scale flow simulation model . Gradual deformation ensures the preservation of the overall geostatistical properties of the fine scale model while upscaling is used as a mandatory step to speed up the simulation proces . We used the gradient method to compute the sensitivity coefficients of the flow simulation results with respect to the coefficients of the gradual deformation . This method requires the petrophysical properties (in this case permeability) to be derivable with respect to these coefficients . When considering facies models, the truncation proces results in discontinuous changes in the model properties and these derivatives cannot be determined . In order to calculate them, we have introduced the concept of transition facies (in addition to the real petrophysical facies) which appears to modify only slightly the upscaled permeability field .We have successfully applied this methodology to integrate interference test data into a 3D geostatistical model containing about two million cells . This validation highlights the capability of this methodology to update directly geostatistical models in a consistent and efficient way .Introductio n

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Section: Principle Of the Methodologymentioning

confidence: 99%

Direct Conditioning of Fine-Scale Facies Models to Dynamic Data by Combining Gradual Deformation and Numerical Upscaling Techniques

Schaaf¹,

Mezghani²,

Chavent³

2002

ECMOR VIII - 8th European Conference on the Mathematics of Oil Recovery

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“…The problem of history matching of reservoir models with unknown geologic facies boundaries has been studied less frequently than the problem of history matching to rock properties (Rahon et al, 1996;Bi, 1999;Landa et al, 2000). Liu and Oliver (2003) applied a gradientbased method to the problem of conditional simulation of facies boundaries generated from Table 2.1: Geostatistical parameters for the gaussian random fields (GRF 1 and GRF 2 ) the truncated plurigaussian method.…”

Section: History Matching Geostatistical Faciesmentioning

confidence: 99%

Data Integration for the Generation of High Resolution Reservoir Models

Reynolds

Oliver

et al. 2009

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The goal of this three-year project was to develop a theoretical basis and practical technology for the integration of geologic, production and time-lapse seismic data in a way that makes best use of the information for reservoir description and reservoir performance predictions. The methodology and practical tools for data integration that were developed in this research project have been incorporated into computational algorithms that are feasible for large scale reservoir simulation models. As the integration of production and seismic data require calibrating geological/geostatistical models to these data sets, the main computational tool is an automatic history matching algorithm. The following specific goals were accomplished during this research. (i) We developed algorithms for calibrating the location of the boundaries of geologic facies and the distribution of rock properties so that production and time-lapse seismic data are honored. (ii) We developed and implemented specific procedures for conditioning reservoir models to time-lapse seismic data. (iii) We developed and implemented algorithms for the characterization of measurement errors which are needed to determine the relative weights of data when conditioning reservoir models to production and time-lapse seismic data by automatic history matching. (iv) We developed and implemented algorithms for the adjustment of relative permeability curves during the history matching process. (v) We developed algorithms for production optimization which accounts for geological uncertainty within the context of closed-loop reservoir management. (vi) To ensure the research results will lead to practical public tools for independent oil companies, as part of the project we built a graphical user interface for the reservoir simulator and history matching software using Visual Basic.iii

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“…Rahon et al 9 investigated two problems in simulating locations of lithofacies conditional to well pressure data. In the first problem, they attempted to estimate the permeability of each facies whose locations have been fixed.…”

Section: Spe 84594mentioning

confidence: 99%

“……………………………….………….. (9) so the gradient of the array f about the Gaussian field Y 1 is a diagonal matrix: Clearly, it is not possible to know the "true" facies type in each gridblock of a field. If provided with a "training image", it should be possible, however, to obtain the pdf of geostatistical model parameters conditional to certain features of facies distribution (see Liu 13 ).…”

Section: Gradient Formulationmentioning

confidence: 99%

Automatic History Matching of Geologic Facies

Liu

Oliver

2003

SPE Annual Technical Conference and Exhibition

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TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractThe truncated pluri-Gaussian method for modeling geologic facies is appealing not only for the wide variety of textures and shapes that can be generated, but also because of the internal consistency of the stochastic model. This method has not, however, been widely applied in simulating distributions of reservoir properties facies or in automatic history matching. One reason seems to be that it is fairly difficult to estimate the parameters of the stochastic model that could be used to generate geological facies maps with the desired properties. The second is that because "facies type" is a discrete variable, it is not straightforward to apply the efficient gradient-based minimization method to generate reservoir facies models that honor production data. Non-gradient methods, however, are too slow for large field-scale problems.In this paper, the non-differentiable history-matching problem was replaced with a differentiable problem so that an automatic history matching technique could be applied to the problem of conditional simulation of facies boundaries generated from the truncated pluri-Gaussian method. The resulting realizations are consistent both with the geostatistical model of the observed facies and the historic production. Application of the method requires efficient computation of the gradient of the objective function with respect to model variables. We present an example five-spot water injection problem with more than 73,000 model variables conditioned to pressure data at wells. The gradient was computed using the adjoint simulator method, and the minimization routine used a quasi-Newton method. The data mismatch decreased more than 90% in the first two iterations.

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Gradients Method Constrained by Geological Bodies for History Matching

Cited by 18 publications

References 0 publications

Direct Conditioning of Fine-Scale Facies Models to Dynamic Data by Combining Gradual Deformation and Numerical Upscaling Techniques

Direct Conditioning of Fine-Scale Facies Models to Dynamic Data by Combining Gradual Deformation and Numerical Upscaling Techniques

Data Integration for the Generation of High Resolution Reservoir Models

Automatic History Matching of Geologic Facies

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