University Research Initiative of

Department of Mathematical Sciences
Department of Petroleum Engineering & Applied Geophysics
Norwegian University of Science & Technology
Trondheim
Norway
 

Vision:

To provide creative mathematical solutions to recognized  challenges in reservoir evaluation.
 

Objectives:

Identify, develop and evaluate mathematically and physically based models for assessment of uncertainties in reservoir evaluation, and distribute information and provide training about these models through education, publishing and seminars.

The activity in the programme is inspired by the problem complexes:
. near-well initial reservoir characterization integrating all available information
. dynamic reservoir characterization based on repeated  seismic monitoring and
   production history
 

Reference persons:

Professor  Henning Omre , Department of Mathematical Sciences, NTNU

Professor  Helge Holden , Department of Mathematical Sciences, NTNU

Professor  Bjørn Ursin , Department of Petroleum Engineering & Applied Geophysics, NTNU

Professor  Ole Torsæter , Department of Petroleum Engineering & Applied Geophysics, NTNU

Professor  Jon Kleppe , Department of Petroleum Engineering & Applied Geophysics, NTNU
 

Ph.d. candidates:

Klaus Dagøe      Jo Eidsvik      Jo Røislien

Stig-Kyrre Foss      (Thomas Theting)
 

Status report:

The current status of the URE-initiative :  Status report
 

Recent publications:

Publications related to the URE activity:

Eidsvik,J.; Avseth,P.; Omre,H.; Mukerji,T. and Mavko,G.; 2001: Stochastic Reservoir Characterization using Pre-stack  Seismic Data; paper submitted for publication
   [copy]

Buland,A. and Omre,H.;2001: Bayesian Wavelet Estimation from Seismic and Well Log Data; extended abstract to appear  in Proceedings from EAGE 63rd Conference and Technical Exhibition; Amsterdam, The Netherlands; June 2001
   [copy]

Kolbjornsen,O. and Omre,H.;2001: Piecewise Affine Inverse Problems; paper  submitted  for publication
    [copy]

Holden,H. and Øksendal,B.;2001: A white noice approach to stochastic Neumannboundary value problems; paper to appear in Festschrift for T.Hilda
    [copy]

Holden,H.; Karlsen,H.K. and Lie,K.A.; 2001: Operator splitting methods for degenerate convection-diffusion equations II: Numerical examples with emphasis on reservoir simulation and sedimentation; paper submitted for publication
   [copy]

Talukdar,S.; Banu,H. ; Torsæter,O. and Kleppe,J.;2000: Applicability and Rate Sensitivity of Several Upscaling Techniques in Fractured Reservoir Simulations; Proceedings from 2000 SPE International Petroleum Conference and Exhibition; Villahermosa, Mexico; Febr. 2000

Jelmert,T.A.; Selseng,H. and Torsæter,O.;2000: Average Permeability Functions of Cores with Stress-Sensitivity; Oil and Gas Journal, Vol.98.24, pp. 52-62; June 2000

Ettrich,N.; Sollid,A. and Ursin,B.;2000: Out-of-plane geometrical spreading in anisotropic media; paper submitted for publication.

Stovas,A. and Ursin,B.;2000: Second order approximations of the reflection and transmission coefficients between two visco-elastic isotropic media; paper submitted for publication.

Brandsberg-Dahl,S,; de Hoop,M.V. and Ursin,B.; 2000: Focusing in dip and AVA compensation on scattering angle/azimuth common image gathers; paper submitted for publication.

Sollid,A. and Ursin,B.; 2000: Scattering-angle migration; Paper submitted for publication.

Helle,H.B.; Bhatt,A. and Ursin,B.; 2000: Porosity and permeability prediction from wireline logs using artificial neural networks. A North Sea case study.

Schleicher,J.; Tygel,M.; Ursin,B. and Bleistein,N.; 2000: The Kirchhoff-Helmholtz integral for anisotropic elastic media; paper submitted for publication.

Ursin,B. and StovasA.; 2000: Reflection and transmission responses of a layered isotropic visco-elastic medium, paper submitted for publication.

Toverud,T.; Dimri,V.P. and Ursin,B.; 2000: Comparison of deconvolution methods for scaling reflectivity; paper submitted for publication.

Causse,E. and Ursin,B.; 2000: Viscoacoustic reverse-time migration; Journal of Seismic Exploration, xx, pp 165-184.

Ursin,B. and Porsani,M.J.; 2000: Estimation of an optimal mixed-phase inverse filter; Geophysical Prospecting, 48, pp 663-676.

Porsani,M.J. and Ursin,B.; 2000: Mixed-phase deconvolution and wavelet estimation; Leading Edge, 19, pp 76-79.

Buland,A. and Omre,H.;2000: Bayesian AVO Inversion ; paper submitted for publication
   [copy]

Borgos,H.G.; Omre,H. and Townsend,C.;2000: Bayes Factors for Model Choice of Fault Size Distribution; paper submitted for publication
   [copy]

Omre,H.;2000: Stochastic Reservoir Models Conditioned to Non-linear Production History Observations; paper to appear in Proceedings from Geostats 2000; Cape Town, South Africa ; April 2000
   [copy]

Borgos,H.G. and Omre;H.;2000: Uncertainty in Fault Geometries; paper to appear in Proceedings from Geostats 2000; Cape Town, South Africa; April 2000
   [copy]

Tweheyo,M.T.; Holt,T. and Torsæter,O.;1999: An Experimental Study of the Relationship between Wettability and Oil Production Characteristics; Journal of Petroleum Science & Engineering, Vol. 24, pp.179-188; Dec. 1999

Lu,G.; Ursin,B. and Lutro,J.; 1999: Model-based removal of water-layer multiple reflections, Geophysics, 64, pp 1816-1827.

Causse,E. and Ursin,B.; 1999: Asymptotic error analysis of constant velocity viscoacoustic migration; Geophysics, 64, pp 1036-1045.

Ekren,B.O. and Ursin,B.; 1999: True-amplitude frequency-wave-number constant-offset migration, Geophysics, 64, pp 915-924.

Tygel,M. and Ursin,B.; 1999: Weak-contrast edge and vertex diffractions in anisotropic elastic media, Wave motion, 29, pp 363-373.

Causse,E,; Mittet,R. and Ursin,B.; 1999: Preconditioned full-waveform inversion in generall viscoacoustic media; Geophysics, 64, pp 130-145.

Hegstad,B.K. and Omre,H.;1999: Uncertainty in Production Forecasts based on Well Observations, Seismic Data and Production History; paper submitted for publication
   [copy]

Eide,A.L.; Omre,H. and Ursin,B.; 1999: Uncertainty in Seismic Inversion for Reservoir Characterization; paper submitted for publication
    [copy]

Holden,H. and Øksendal,B.;1999: A white noise approach to stochastic differential equations driven by Wiener and Poisson processes; in Nonlinear Theory of Generalized Functions; Eds. Grosser, Hormann, Kunziger and Obenguggenberger; Chapmann and Hall.
    [copy]

Holden,H.; Øksendal,B.; Ubøe,J. and Zhang,T.S.;1996: Stochastic Partial Differential Equations; Birkhauser Verlag
 

URE-seminar topics:

The following topics are offered as in-house seminars for the participants:

Inversion of seismic AVO-data
by  Henning Omre/ Bjørn Ursin

Repeated seismic monitoring requires the use of AVO-data in order to classify pore fluids. These data are
associated with considerable uncertainty, hence a statistical approach seems reasonable. Various Bayesian
inversion techniques will be presented and demonstrated.

Scattering-angle/azimuth common image gathers
by Bjørn Ursin

Common image gathers (CIGs) in the offset and surface azimuth domain are used extensively in migration velocity analysis and amplitude versus offset studies. If the geology is complex and the rayfield becomes multi-pathed, the quality of the CIG's deteriorates. To overcome these problems, the CIGs may instead be generated as a function of scattering-angle and azimuth at the image point.  The metodology for doing this will be presented with several case studies.
 

Matching of production history
by  Henning Omre

Production forecasts are crucial for reliable reservoir management. These forcasts should be based on all available
reservoir specific observations. Conditioning on production history causes particular problems. Various stochastic
approaches to history matching will be presented and demonstrated.
 

Front tracking for hyperbolic conservation laws - theory and numerics
by Helge Holden

Hyperbolic conservation laws are the fundamental differential equations used in modelling of fluid flow in porous media. Front tracking constitutes one method by which one can develope both numerical techniques and analytical results. The numerical methods are used in commercial packages. Both analytical results and more applied aspects will be emphasized.
 

Stochastic partial differential equations
by Helge Holden

It is quite common to model the lack of information conserning flow in porous media by stochastic equations, replacing quantitative information by stochastic information. This results in stochastic partial differential equations. A general framework for studying classes of such equations is provided by the so-called white noice analysis.  These techniques will be presented, and one may focus on particular types of equations.
 

Wettability in petroleum reservoirs
by Ole Torsæter

The wettability has influence on the recovery of reservoirs.  Measuring the wettability is complicated. Various methods for wettability prediction from core plugs and  in situ in the reservoir will be presented.  Moreover, the influence of wettability on fluid distribution in homogeneous and heterogeneous reservoirs will be discussed.  Examples of  the wettabilities influence on the production characteristics will be presented.
 

Research links: