Research Director
Petter Abrahamsen
- Department Statistical analysis of natural resource data
- Mobile phone +47 917 45 547
- Phone number +47 22 85 26 40
- E-mail pab@nr.stage.dekodes.no
Publications
- 197 publications found
Abrahamsen, Petter; Dahle, Pål; Nevjen, Fredrik; Kvernelv, Vegard; Sektnan, Audun; Vazquez, Ariel Almendral; Waade, Bendik Skundberg og Aarnes, Ingrid. (2025).
COHIBA User Manual Version 7.2.1.
Vis sammendrag
This user manual describes the COHIBA surface modeling software. It consists of:
Part I Introduction: Basic ideas and terminology
Part II User manual: Usage, input data, and results
Part III Tutorials: Special topics such as volumes, simulation, and faults
Part IV Reference manual: Descriptions of all COHIBA model file elements
Part V Theory: Methods used by COHIBA
Part VI Appendix: Release notes, known issues, references, list of acronyms,
tables and figures, and an index
Abrahamsen, Petter; Dahle, Pål; Nevjen, Fredrik; Kvernelv, Vegard; Sektnan, Audun; Vazquez, Ariel Almendral; Waade, Bendik Skundberg og Aarnes, Ingrid. (2025).
Cohiba User Manual Version 7.2.
Vis sammendrag
This user manual describes the COHIBA surface modeling software. It consists of:
Part I Introduction: Basic ideas and terminology
Part II User manual: Usage, input data, and results
Part III Tutorials: Special topics such as volumes, simulation, and faults
Part IV Reference manual: Descriptions of all COHIBA model file elements
Part V Theory: Methods used by COHIBA
Part VI Appendix: Release notes, known issues, references, list of acronyms,
tables and figures, and an inde
Kjønsberg, Heidi; Barker, Daniel Martin L; Fjeldstad, Torstein Mæland; Fjellvoll, Bjørn; Hauge, Ragnar; Nilsen, Carl-Inge Colombo; Røe, Per; Sanchis, Charlotte Juliette; Solberg, Eilif og Abrahamsen, Petter. (2025).
GIG annual meeting 2025 - Summary of 2024 and planned work for 2025.
NVA
Rapport
Barker, Daniel Martin L; Fjeldstad, Torstein Mæland; Fjellvoll, Bjørn; Hauge, Ragnar; Kjønsberg, Heidi; Nilsen, Carl-Inge Colombo; Røe, Per; Semin-Sanchis, Charlotte Juliette; Solberg, Eilif og Abrahamsen, Petter. (2024).
PCube User Manual Version 10.5.
NVA
Rapport
Aker, Eyvind; Barker, Daniel Martin L; Fjeldstad, Torstein Mæland; Fjellvoll, Bjørn; Hauge, Ragnar; Kjønsberg, Heidi; Nilsen, Carl-Inge Colombo; Røe, Per; Semin-Sanchis, Charlotte Juliette og Abrahamsen, Petter. (2024).
GIG annual meeting 2024 - summary of 2023 and planned work for 2024.
NVA
Rapport
Vazquez, Ariel Almendral; Dahle, Pål; Abrahamsen, Petter og Sektnan, Audun. (2024).
Consistent prediction of well paths and geological surfaces.
Vis sammendrag
We propose a smooth stochastic process for modeling the vertical well path uncertainty. This process describes the accumulation of measurement errors along the well path. We combine the stochastic process with a stochastic model for surfaces into a consistent framework for simultaneous prediction of well paths and surfaces. We show properties of the proposed stochastic process and provide examples of interaction between wells and surfaces.
Abrahamsen, Petter. (2024).
Norwegian Computing Center, Joining Forces: Solving the energy challenges together. FORCE, Norwegian Offshore Directorate
NVA
Faglig foredrag
Lilleborge, Marie; Hauge, Ragnar; Fjellvoll, Bjørn og Abrahamsen, Petter. (2024).
Using Pattern Counts to Quantify the Difference Between a Pair of Three-Dimensional Realizations.
Vis sammendrag
When comparing different ways of modeling discrete three-dimensional realizations such as facies, it is useful to have a measure of difference (or similarity) in the geometry of these realizations.We propose a method for evaluating such difference by comparing pattern counts for a small template. Tests on synthetic datasets demonstrate that the proposed difference effectively differentiates between realizations of a Boolean model and those generated using multiple-point statistics with the Boolean realizations as training images. We also observed that multiple-point statistics realizations based on similar training images yield smaller differences to one another compared to those based on training images from dissimilar concepts. This suggests that the proposed difference is a useful tool for comparing discrete three-dimensional realizations.
Aker, Eyvind; Barker, Daniel Martin L; Fjeldstad, Torstein Mæland; Fjellvoll, Bjørn; Hauge, Ragnar; Kjønsberg, Heidi; Nilsen, Carl-Inge Colombo; Røe, Per; Semin-Sanchis, Charlotte Juliette og Abrahamsen, Petter. (2023).
PCube reference manual.
NVA
Rapport
Aker, Eyvind; Barker, Daniel Martin L; Fjeldstad, Torstein Mæland; Fjellvoll, Bjørn; Hauge, Ragnar; Kjønsberg, Heidi; Nilsen, Carl-Inge Colombo; Røe, Per; Semin-Sanchis, Charlotte Juliette og Abrahamsen, Petter. (2023).
PCube User Manual version 10.0.
NVA
Rapport
Abrahamsen, Petter. (2023).
Uncertainty, probability and bad luck. Sharp Reflections
NVA
Faglig foredrag
Aker, Eyvind; Barker, Daniel Martin L; Fjeldstad, Torstein Mæland; Hauge, Ragnar; Kjønsberg, Heidi; Nilsen, Carl-Inge Colombo; Røe, Per; Sanchis, Charlotte Juliette og Abrahamsen, Petter. (2022).
GIG annual meeting 2022 - Summary of 2021 and planned work for 2022.
NVA
Rapport
Vis sammendrag
The GIG, Geophysical Inversion to Geology, consortium is a research consortium run by Norwegian Computing Center, with the aim of developing new understanding, new methods and software for obtaining reservoir properties from geophysical measurements
This note gives a summary of the work in 2021 and the suggested work plan for 2022. The final work plan for 2022 will be decided on the annual meeting in Jan 2022.
Vazquez, Ariel Almendral; Dahle, Pål; Abrahamsen, Petter og Sektnan, Audun. (2022).
Conditioning geological surfaces to horizontal wells.
Lilleborge, Marie; Fjellvoll, Bjørn; Hauge, Ragnar og Abrahamsen, Petter. (2021).
Assessing Multiple-Point Statistics by use of pattern counts to compare images.
NVA
Rapport
Løland, Anders; Abrahamsen, Petter og Dahle, Pål. (2021).
Fra verdifulle oljefelt til farlige løsmasser med COHIBA.
NVA
Programdeltagelse
Røe, Per; Aker, Eyvind; Barker, Daniel Martin L; Fjeldstad, Torstein Mæland; Hauge, Ragnar; Kjønsberg, Heidi; Nilsen, Carl-Inge Colombo; Sanchis, Charlotte Juliette og Abrahamsen, Petter. (2021).
GIG annual meeting 2021 - Summary of 2020 and planned work for 2021.
NVA
Rapport
Vis sammendrag
The GIG, Geophysical Inversion to Geology, consortium is a research consortium run by Norwegian Computing Center, with the aim of developing new understanding, new methods and software for obtaining reservoir properties from geophysical measurements
This note gives a status of the GIG consortium after its fourth year of operation, and also gives the suggested work plan for 2021.
Kvernelv, Vegard Berg; Aarnes, Ingrid og Abrahamsen, Petter. (2021).
Geostatistisk kartlegging av løsmasser.
NVA
Rapport
Sektnan, Audun; Abrahamsen, Petter og Dahle, Pål. (2020).
Dip point coordinates in COHIBA.
NVA
Rapport
Abrahamsen, Petter; Dahle, Pål; Kvernelv, Vegard Berg; Sektnan, Audun; Vazquez, Ariel Almendral og Aarnes, Ingrid. (2020).
COHIBA User Manual Version 6.1.
NVA
Rapport
Røe, Per; Hauge, Ragnar; Aker, Eyvind; Barker, Daniel Martin L; Nilsen, Carl-Inge Colombo; Sanchis, Charlotte Juliette; Kjønsberg, Heidi; Abrahamsen, Petter og Nesvold, Erik. (2020).
GIG annual meeting 2020
Summary of 2019 and planned work for 2020.
NVA
Rapport
Vazquez, Ariel Almendral; Dahle, Pål og Abrahamsen, Petter. (2020).
Compendium of Linvel formulas used in Cohiba.
NVA
Rapport
Goodwin, Håvard; Lilleborge, Marie og Abrahamsen, Petter. (2020).
Decision Nodes - Uncertainty propagation in decision trees.
NVA
Rapport
Sektnan, Audun; Dahle, Pål; Vazquez, Ariel Almendral og Abrahamsen, Petter. (2019).
Getting the zonation right. A synthetic real-time case study. Norsk Regnesentral
NVA
Faglig foredrag
Vis sammendrag
A COHIBA case study investigating a synthetic model for depth conversion, with focus on how to get the zonation right and the impact of different modelling settings on the estimation of volume distributions.
Abrahamsen, Petter. (2019).
Volume estimation, simulation and rejection sampling - Some rarely used COHIBA features. Norsk Regnesentral
NVA
Faglig foredrag
Abrahamsen, Petter. (2019).
A historic perspective on Bayesian surface modelling. Norsk Regnesentral
NVA
Faglig foredrag
Fjellvoll, Bjørn; Hauge, Ragnar; Vazquez, Ariel Almendral; Abrahamsen, Petter og Skauvold, Jacob. (2019).
Applied Geostatistics and Geomodelling 2019. Equinor
NVA
Faglig foredrag
Abrahamsen, Petter. (2019).
COHIBA - Consistent, robust, and accurate prediction of surfaces. Norsk Regnesentral
NVA
Faglig foredrag
Dahle, Pål; Abrahamsen, Petter og Vazquez, Ariel Almendral. (2019).
Handling true vertical depth (TVD) uncertainty in wells. Norsk Regnesentral
NVA
Faglig foredrag
Vis sammendrag
We have developed a model for the true vertical depth (TVD) uncertainty in wells. The model allows well positions to be predicted given the well uncertainty and surface uncertainties. From this, we can predict the most likely position of the well.
Vazquez, Ariel Almendral; Aarnes, Ingrid og Abrahamsen, Petter. (2019).
Application of NR’s Solutions to Geothermal Reservoir Characterization.
NVA
Rapport
Røe, Per; Hauge, Ragnar; Aker, Eyvind; Barker, Daniel Martin L; Nilsen, Carl-Inge Colombo; Sanchis, Charlotte Juliette; Kjønsberg, Heidi og Abrahamsen, Petter. (2019).
GIG annual meeting 2019 - Summary of 2018 and planned work for 2019.
NVA
Rapport
Vazquez, Ariel Almendral; Abrahamsen, Petter; Dahle, Pål og Sektnan, Audun. (2019).
A novel implementation of the LinVel model. Norsk Regnesentral
NVA
Faglig foredrag
Vazquez, Ariel Almendral; Abrahamsen, Petter; Dahle, Pål og Sektnan, Audun. (2019).
Getting the most out of your deep directional resistivity data. Norsk Regnesentral
NVA
Faglig foredrag
Abrahamsen, Petter. (2019).
Machine learning - Finding Cut Rocks and Cute Animals. SINTEF
NVA
Faglig foredrag
Dahle, Pål; Aarnes, Ingrid; Abrahamsen, Petter; Vazquez, Ariel Almendral og Sektnan, Audun. (2019).
Increasing subsurface accuracy with COHIBA by taking advantage of resistivity contrasts.
NVA
Rapport
Abrahamsen, Petter. (2019).
Kriging Derivatives.
Vis sammendrag
Some properties of conditioning a Gaussian random field on point value data and derivative data is investigated. Linear predictors with or without a linear trend are considered. Derivative data are seen to improve predictions and the corresponding prediction errors are reduced. The predictors are extensions to the well known simple and universal kriging predictors. The covariance functions between different components of the derivative fields are the key component entering the predictors. They are given by partial derivatives of the covariance function of the Gaussian random field. Spatial symmetries such as stationarity and isotropy are used to restrict the number of covariance functions. In particular isotropy reduces complexity and a general framework for utilising this spatial symmetry is established. Properties of the predictors and the associated prediction error are studied in detail for some particular isotropic covariance functions. The importance of the smoothness of the random field on the predictor and the prediction error is
illustrated. This text was first published as part of Abrahamsen (1997).
Abrahamsen, Petter; Dahle, Pål; Kvernelv, Vegard Berg; Sektnan, Audun; Vazquez, Ariel Almendral og Aarnes, Ingrid. (2019).
COHIBA User Manual Version 6.0.
Vis sammendrag
This user manual describes the COHIBA surface modeling software. It consists of:
Part I Introduction: Basic ideas and terminology
Part II User manual: Usage, input data and results
Part III Tutorials: Special topics such as volumes, simulation and faults
Part IV Reference manual: Descriptions of all COHIBA model file elements
Part V Theory: Methods used by COHIBA
Part VI Appendix: Release notes, known issues, references, list of acronyms,
tables and figures, and an index
Advanced topics and technicalities are marked by the warning symbol in the right margin. COHIBA model file elements marked by this warning symbol should be used with some care. The latest version of this document is available at: www.nr.no/COHIBA. For COHIBA support contact Pal.Dahle@nr.no or Ariel.Almendral.Vazque@nr.no.
The following scientists at Norwegian Computing Center has contributed to the development of
COHIBA:
Petter Abrahamsen
Pål Dahle Frode Georgsen
Vera Louise
Hauge Gudmund Hermansen
Odd Kolbjørnsen
Lars Bakke Krogvik
Vegard Berg Kvernelv
Inge Myrseth
Audun Sektnan
Arne Skorstad
Harald Soleng
Ariel Almendral Vazquez
Maria Vigsnes
Ingrid Aarnes
The front page shows two fences along well paths on top of a faulted surface on the Valhall carbonate field in the North Sea. The illustration is made by Ingrid Aarnes. We thank Aker BP for permission to publish the illustration.
Abrahamsen, Petter. (2019).
Modelling Techniques. Norsk Petroleumsforening
NVA
Faglig foredrag
Vis sammendrag
An overview over different techniques for making numerical reservoir models.
Aker, Eyvind; Røe, Per; Hauge, Ragnar og Abrahamsen, Petter. (2019).
PCube+ principles. Sharp Reflections
NVA
Faglig foredrag
Aker, Eyvind; Røe, Per; Hauge, Ragnar og Abrahamsen, Petter. (2019).
PCube+ principles. Sharp Reflections
NVA
Faglig foredrag
Kvernelv, Vegard Berg; Barker, Daniel Martin L og Abrahamsen, Petter. (2018).
Simulation of Gaussian Random Fields Using the Fast Fourier Transform.
NVA
Rapport
Abrahamsen, Petter; Vazquez, Ariel Almendral; Dahle, Pål; Kvernelv, Vegard Berg og Sektnan, Audun. (2018).
Cohiba User Manual Version 5.6.
NVA
Rapport
Abrahamsen, Petter; Kvernelv, Vegard Berg og Barker, Daniel Martin L. (2018).
Simulation of Gaussian Random Fields Using the Fast Fourier Transform (FFT).
Vis sammendrag
We generate independent Gaussian random variables on a regular grid and use a spatial filter to smooth the independent random variables to obtain a spatially correlated Gaussian random field. The FFT is used to speed up the smoothing since convolution is a simple cell by-cell multiplication in the Fourier domain. A representation of the spatial convolution filter in the Fourier domain is efficiently obtained from the FFT of any stationary correlation function. Since FFT is cyclic, the grid must be padded to ensure that opposite sides are uncorrelated. The size of the padding is discussed in detail. Most standard covariance functions fail to be positive definite on finite cyclic domains. This causes striping artifacts in the final simulated realizations and failure to meet statistical properties such as variogram reproduction in the simulated realizations. These problems are addressed and solutions are provided to ensure near perfect statistical properties of the generated realizations. The method is fast and can generate a hundred million grid cell realization in approximately 1.5 minutes on a standard laptop PC. The method scales approximately linearly in the number of grid cells.
Dahle, Pål; Vazquez, Ariel Almendral og Abrahamsen, Petter. (2018).
COHIBA and velocity models linear in depth.
NVA
Rapport
Abrahamsen, Petter; Dahle, Pål; Kvernelv, Vegard Berg; Sektnan, Audun og Vazquez, Ariel Almendral. (2017).
Cohiba User Manual Version 5.5.
NVA
Rapport
Røe, Per; Hauge, Ragnar; Aker, Eyvind; Abrahamsen, Petter; Hauge, Vera Louise og Sanchis, Charlotte Juliette. (2017).
GIG annual meeting 2018
Summary of 2017 planned work for 2018.
NVA
Rapport
Vigsnes, Maria; Kolbjørnsen, Odd; Hauge, Vera Louise; Dahle, Pål og Abrahamsen, Petter. (2017).
Fast and Accurate Approximation to Kriging Using Common Data Neighborhoods.
Vis sammendrag
Unknown values of a random field can be predicted from observed data using kriging. As data sets grow in size, the computation times become large. To facilitate kriging with large data sets, an approximation where the kriging is performed in sub-segments with common data neighborhoods has been developed. It is shown how the accuracy of the approximation can be controlled by increasing the common data neighborhood. For four different variograms, it is shown how large the data neighborhoods must be to get an accuracy below a chosen threshold, and how much faster these calculations are compared to the kriging where all data are used. Provided that variogram ranges are small compared to the domain of interest, kriging with common data neighborhoods provides excellent speed-ups (2–40) while maintaining high numerical accuracy. Results are presented both for data neighborhoods where the neighborhoods are the same for all sub-segments, and data neighborhoods where the neighborhoods are adapted to fit the data densities around the sub-segments. Kriging in sub-segments with common data neighborhoods is well suited for parallelization and the speed-up is almost linear in the number of threads. A comparison is made to the widely used moving neighborhood approach. It is demonstrated that the accuracy of the moving neighborhood approach can be poor and that computational speed can be slow compared to kriging with common data neighborhoods.
Abrahamsen, Petter; Dahle, Pål; Hauge, Vera Louise; Hermansen, Gudmund Horn; Kvernelv, Vegard Berg og Vazquez, Ariel Almendral. (2016).
Cohiba User Manual Version 5.4.
NVA
Rapport
Fjellvoll, Bjørn; Abrahamsen, Petter; Hauge, Ragnar og Vazquez, Ariel Almendral. (2016).
Geostatistics course. Statoil
NVA
Faglig foredrag
Abrahamsen, Petter; Dahle, Pål; Hauge, Vera Louise; Hermansen, Gudmund Horn; Vigsnes, Maria og Almendral-Vazquez, Ariel. (2015).
Cohiba User Manual
Version 5.3.
NVA
Rapport
Abrahamsen, Petter; Dahle, Pål; Hauge, Vera Louise; Hermansen, Gudmund Horn; Vigsnes, Maria og Vazquez, Ariel Almendral. (2015).
Cohiba User Manual, Version 5.1.
NVA
Rapport
Abrahamsen, Petter; Dahle, Pål; Hauge, Vera Louise; Hermansen, Gudmund Horn; Vigsnes, Maria og Almendral-Vazquez, Ariel. (2015).
Cohiba User Manual
Version 5.2.
NVA
Rapport
Dahle, Pål; Abrahamsen, Petter og Almendral-Vazquez, Ariel. (2015).
Simultaneous prediction of geological surfaces and well paths. European Association of Geoscientists and Engineers (EAGE)
Dahle, Pål; Abrahamsen, Petter og Almendral-Vazquez, Ariel. (2015).
Simultaneous prediction of geological surfaces and well paths. Roxar
NVA
Faglig foredrag
Abrahamsen, Petter; Dahle, Pål; Hauge, Vera Louise; Vazquez, Ariel Almendral og Vigsnes, Maria. (2015).
Surface prediction using rejection sampling
to handle non-linear constraints.
Vis sammendrag
We demonstrate accurate prediction of geological surfaces by imposing consistent physical and stochastic relationships between surfaces. The accuracy is improved by using all relevant information collected in wells: well points, zonation in horizontal sections, and gas/fluid content along wells. The conditioned surfaces are used to provide estimates of gross rock volumes of oil and gas reservoirs. In particular, it is shown how knowledge of spill point and zonation along well paths affect trapped volumes. A plain rejection sampling technique is used to deal with the highly non-linear relationships between a surface and its spill point. For well path conditioning, an extension of kriging to treat inequality constraints is proposed. It is based on efficient rejection sampling from a high dimensional truncated multivariate Gaussian distribution. The impact on gross rock volume distributions from different assumptions and data types is demonstrated by examples and the uncertainties in all the involved data types are consistently handled and quantified.
Vigsnes, Maria; Abrahamsen, Petter; Hauge, Vera Louise og Kolbjørnsen, Odd. (2015).
Efficient Neighborhoods for Kriging with Numerous Data. EAGE
Vis sammendrag
Kriging is a data interpolation method that can be used to populate regular grids from data scattered in space, and requires the solution of a linear equation system the size of the number of data. When the data is numerous the speed of the calculation is slow. In this paper we propose to divide the regular grid into rectangular sub-segments and let all the grid cells in each sub-segment share a common data neighborhood. The advantage of this approach is that the number of data in the neighborhoods can be small compared to the complete dataset and it is possible to reuse some of the computations for all grid cells in each sub-segment. We show that the precision can be controlled through selection of neighbourhood size, and that the speed of the calculations can be optimized through selection of subsegment size. We show that this is an efficient method for kriging when number of data is huge, giving a significant speed-up even for high data densities and precisions.
Vigsnes, Maria og Abrahamsen, Petter. (2015).
Depth conversion on the Johan Sverdrup Oil field - using Cohiba.
NVA
Rapport
Vigsnes, Maria og Abrahamsen, Petter. (2015).
Detailed analyses for Cohiba depth conversion on the Johan Sverdrup Oil Field.
NVA
Rapport
Almendral-Vazquez, Ariel; Abrahamsen, Petter; Dahle, Pål og Hermansen, Gudmund Horn. (2015).
A continuous model for well depths: theory and application to well repositioning. Norsk statistikk forening
NVA
Vitenskapelig foredrag
Dahle, Pål; Abrahamsen, Petter og Almendral-Vazquez, Ariel. (2015).
Surface modelling in fault blocks using COHIBA: A feasibility study.
NVA
Rapport
Fjellvoll, Bjørn; Hauge, Ragnar; Abrahamsen, Petter og Almendral-Vazquez, Ariel. (2015).
Four days course in Geostatistics and Advanced Geomodelling. Norsk Regnesentral
NVA
Faglig foredrag
Vigsnes, Maria og Abrahamsen, Petter. (2014).
Detailed analysis for Cohiba depth conversion on the Johan Sverdrup Field Rev. 2.
NVA
Rapport
Røe, Per; Georgsen, Frode og Abrahamsen, Petter. (2014).
An Uncertainty Model for Fault Shape and Location.
Vis sammendrag
Fault models are often based on interpretations of seismic data that are constrained by observations of faults and associated strata in wells. Because of uncertainties in depth migration, seismic interpretations and well data, there often is significant uncertainty in the geometry and position of the faults. Fault uncertainty impacts determinations of reservoir volume, flowproperties and well planning. Stochastic simulation of the faults is important for quantifying the uncertainties and minimizing the impacts. In this paper, a framework for representing and modeling uncertainty in fault location and geometry is presented. This framework can be used for prediction andstochastic simulation of fault surfaces, visualization of fault location uncertainty, and assessments of the sensitivity of fault location on reservoir performance. The uncertainty in fault location is represented by a fault uncertainty envelope and a marginal probability distribution. To be able to use standard geostatistical methods, quantile mapping is employed to construct a transformation from the fault surface domain to a transformed domain. Well conditioning is undertaken in the transformed domain using kriging or conditional simulations. The final fault surface is obtained by transforming back to the fault surface domain. Fault location uncertainty can be visualized by transforming the surfaces associated with a given quantile back to the fault surface
domain.
Abrahamsen, Petter; Dahle, Pål; Hauge, Vera Louise; Almendral-Vazquez, Ariel og Vigsnes, Maria. (2014).
Surface prediction using rejection sampling to handle non-linear relationships. Canadian Society of Petroleum Geologists (CSPG)
NVA
Vitenskapelig foredrag
Vis sammendrag
We demonstrate accurate surface predictions by imposing consistent physical and stochastic relationships between surfaces. The accuracy is improved by using all relevant information collected in wells: well markers, zone logs in horizontal sections, and gas/fluid content along wells. The conditioned surfaces are used to provide estimates of gross rock volumes of oil and gas reservoirs. In particular, we show how spill point and zone log information affect trapped volumes. We apply plain rejection sampling techniques to deal with the highly non-linear relationships between a surface and its spill point. For well path conditioning we build upon an extension of kriging to treat inequality constraints, based on an efficient rejection sampling from a high dimensional truncated multivariate Gaussian distribution. A fast approximate approach to simulating surfaces is presented and successfully applied to estimate volumes. The impact on gross rock volume distributions from different assumptions and data types is demonstrated by several examples and the uncertainties in all the involved data types are consistently handled and quantified.
Abrahamsen, Petter; Dahle, Pål; Hauge, Vera Louise og Vigsnes, Maria. (2014).
Impact on Gross-Rock Volume Distributions from Uncertainties in Surfaces and Hydrocarbon Contacts. European Association of Geoscientists and Engineers (EAGE)
NVA
Vitenskapelig foredrag
Vis sammendrag
The gross-rock volume often accounts for the largest uncertainty in reserves. It is therefore important to obtain a correct gross-rock volume distribution and to reduce the uncertainty by using all available data. We demonstrate a way of obtaining accurate volume estimates by imposing realistic and consistent physical and stochastic relationships between the surfaces and hydrocarbon contacts that define the reservoir rock volume. The uncertainty is reduced by using all relevant information collected in wells; well markers, zone logs in horizontal sections, and gas/fluid content along wells. Uncertainties in all these data types are handled. The impact on volume distributions from different assumptions and data types are demonstrated by several examples. We will in particular demonstrate how restrictions on the possible spill point depth have impact on the potential trap size and the trapped volume. Some of the results are obtained using standard stochastic simulation (Monte Carlo) techniques but in particular the highly non-linear relationship between a surface and its spill point requires rejection sampling techniques. Rejection sampling is simple but very inefficient so a fast approximate approach to simulating surfaces is investigated. The conclusion is that the approximation works for calculating volumes but individual surface realizations have unacceptable artefacts.
Abrahamsen, Petter; Dahle, Pål; Georgsen, Frode; Hermansen, Gudmund Horn og Myrseth, Inge. (2013).
Cohiba User Manual Version 4.1.
NVA
Rapport
Abrahamsen, Petter. (2013).
SAND 2013 - Kiel.
NVA
Rapport
Vis sammendrag
Referat fra SAND's gruppesamling 2013.
Abrahamsen, Petter. (2013).
Norsk Regnesentral(NR)/Norwegian Computing Center. FORCE
NVA
Faglig foredrag
Vis sammendrag
Overview of NR's activities within oil & gas.
Kolbjørnsen, Odd; Stien, Marita; Kjønsberg, Heidi; Fjellvoll, Bjørn og Abrahamsen, Petter. (2013).
Using Multiple Grids in Markov Mesh Facies Modeling.
Vis sammendrag
A multigrid Markov mesh model for geological facies is formulated by defining a hierarchy of nested grids and defining a Markov mesh model for each of these grids. The facies probabilities in the Markov mesh models are formulated as generalized linear models that combine functions of the grid values in a sequential neighborhood. The parameters in the generalized linear model for each grid are estimated from the training image. During simulation, the coarse patterns are first laid out, and by simulating increasingly finer grids we are able to recreate patterns at different scales. The method is applied to several tests cases and results are compared to the training image and the results of a commercially available snesim algorithm. In each test case, simulation results are compared qualitatively by visual inspection, and quantitatively by using volume fractions, and an upscaled permeability tensor. When compared to the training image, the method produces results that only have a few percent deviation from the values of the training image. When compared with the snesim algorithm the results in general have the same quality. The largest computational cost in the multigrid Markov mesh is the estimation of model parameters from the training image. This is of comparable CPU time to that of creating one snesim realization. The simulation of one realization is typically ten times faster than the estimation.
Abrahamsen, Petter; Dahle, Pål; Hauge, Vera Louise; Hermansen, Gudmund Horn og Vigsnes, Maria. (2013).
COHIBA technical manual (SAND/12/13).
NVA
Rapport
Abrahamsen, Petter; Dahle, Pål; Hermansen, Gudmund Horn; Hauge, Vera Louise og Vigsnes, Maria. (2013).
COHIBA user manual version 4.2 (SAND/10/13).
NVA
Rapport
Stenerud, Vegard Røine; Kallekleiv, Hans Ivar; Abrahamsen, Petter; Dahle, Pål; Skorstad, Arne og Viken, May Hege Aalmen. (2012).
Added Value by Fast and Robust Conditioning of Structural Surfaces to Horizontal Wells for Real-World Reservoir Models.
Vis sammendrag
Structural updates for a complex reservoir model require time-consuming manual work, therefore, updates are rarely performed. This leads to an outdated model that gradually loses its predictability. Eventually, this results in model breakdown, and a new model must be built from scratch. Continuously updatable reservoir models avoid this and increase the value of models as a tool in decision making. In addition, easily updateable structural surfaces enable several structural realizations for spanning the uncertainty.
We present the use of a method for fast and robust updates of structural surfaces in reservoir models. We will focus on updates using zone data from horizontal wells (zone-log conditioning), since this traditionally has been a bottleneck that needs tedious manual work prone to error. In zone-log conditioning, we try to generate horizon surfaces that honor the geological zonation along the well paths. This is important for property modeling, and is crucial for fluid-flow simulations. Our method is robust, fully automated, and is built on a consistent mathematical framework that includes specified input-data uncertainties. It has provided satisfactory results for large real-world reservoir models where standard methods and work processes have failed. The field example presented shows a reduction from 22.9 % to 0.9 % in incorrectly honoring of the zone logs by applying this method rather than the standard approach. The remaining 0.9 % is due to conflicting data, gridding errors, and is difficult to get rid of even with manual editing. We consider this a large step forward with respect to providing an up-to-date basis for decisions that also can account for structural uncertainties.
Almendral-Vazquez, Ariel; Dahle, Pål; Abrahamsen, Petter; Georgsen, Frode og Myrseth, Inge. (2012).
Cohiba User Manual Version 3.1.1.
NVA
Rapport
Abrahamsen, Petter; Dahle, Pål; Georgsen, Frode og Myrseth, Inge. (2012).
Cohiba User Manual Version 4.0.
NVA
Rapport
Syversveen, Anne Randi; Abrahamsen, Petter; Tveranger, Jan; Nilsen, Halvor Møll og Lie, Knut-Andreas. (2012).
A Study on How Cap Rock Geometry Influences the CO2 Storage Capacity. The Geological Society
NVA
poster
Abrahamsen, Petter; Kolbjørnsen, Odd og Hauge, Ragnar. (2012).
Geostatistics Oslo 2012.
NVA
Vitenskapelig antologi/Konferanseserie
Abrahamsen, Petter; Dahle, Pål og Skorstad, Arne. (2012).
A Fast and Consistent Geostatistical Approach for Constraining 3D Structural Models to Horizontal Wells. EAGE - European Association of Geoscientists & Engineers
NVA
Vitenskapelig foredrag
Vis sammendrag
The use of horizontal well data in 3D reservoir modeling has become an increasingly important task as the use of horizontal wells has become common practice. Standard gridding approaches are based on the use of well picks to define the positions of stratigraphic surfaces along well bores. Horizontal wells however, are often drilled almost parallel to the stratigraphic layering so the number of horizons intersected along a horizontal well can be relatively few. Therefore, horizontal sections of the well can be used to constrain the structural position of reservoir zones. A robust, geostatistical approach has been developed to ensure consistent use of horizontal well data in the construction of 3D structural models. Kriging is used for prediction of surface location based on well picks and constraints obtained from zone logs along horizontal wells. In contrast to standard approaches, all well data (picks and constraints) from all surfaces are treated simultaneously and will have impact on all surfaces above and below. The geostatistical approach is fast and reproducible, and allows structural models to be updated continuously as new wells are drilled. The uncertainty can be evaluated by kriging error maps or by generating stochastic realizations that honor all the well data.
Syversveen, Anne Randi; Nilsen, Halvor Møll; Lie, Knut-Andreas; Tveranger, Jan og Abrahamsen, Petter. (2012).
A Study of How Top-Surface Morphology Influences the Storage Capacity of CO2 in Saline Aquifers. Norwegian Computing Center/University of Oslo
NVA
Vitenskapelig foredrag
Vis sammendrag
The primary trapping mechanism in CO2 storage is structural trapping, which means accumulation of a CO2 column under a deformation in the caprock. We present a study on how different top-seal morphologies will influence the CO2 storage capacity and migration patterns. Alternative top-surface morphologies are created stochastically by combining different stratigraphic scenarios with different structural scenarios. Stratigraphic surfaces are generated by Gaussian random fields, while faults are generated by marked point processes. The storage capacity is calculated by a simple and fast spill-point analysis, and by a more extensive method including fluid flow simulation in which parameters such as pressure and injection rate are taken into account. Results from the two approaches are compared. Moreover, by generating multiple realizations, we quantify how uncertainty in the top-surface morphology impacts the primary storage capacity. The study shows that the morphology of the top seal is of great importance both for the primary storage capacity and for migration patterns.
Syversveen, Anne Randi; Nilsen, Halvor Møll; Lie, Knut-Andreas; Tveranger, Jan og Abrahamsen, Petter. (2012).
A Study on How Top-Surface Morphology Influences the Storage Capacity of CO2 in Saline Aquifers.
Vis sammendrag
The primary trapping mechanism in CO2 storage is structural trapping, which means accumulation of a CO2 column under a deformation in the caprock. We present a study on how different top-seal morphologies will influence the CO2 storage capacity and migration patterns. Alternative top-surface morphologies are created stochastically by combining different stratigraphic scenarios with different structural scenarios. Stratigraphic surfaces are generated by Gaussian random fields, while faults are generated by marked point processes. The storage capacity is calculated by a simple and fast spill-point analysis, and by a more extensive method including fluid flow simulation in which parameters such as pressure and injection rate are taken into account. Results from the two approaches are compared. Moreover, by generating multiple realizations, we quantify how uncertainty in the top-surface morphology impacts the primary storage capacity. The study shows that the morphology of the top seal is of great importance both for the primary storage capacity and for migration patterns.
Almendral-Vazquez, Ariel; Dahle, Pål; Abrahamsen, Petter; Georgsen, Frode og Myrseth, Inge Bjørn. (2011).
Cohiba user manual Version 2.5.
NVA
Rapport
Almendral-Vazquez, Ariel; Abrahamsen, Petter; Dahle, Pål; Georgsen, Frode og Myrseth, Inge Bjørn. (2011).
COHIBA user manual - Version 2.4.
NVA
Rapport
Almendral-Vazquez, Ariel; Dahle, Pål; Abrahamsen, Petter; Georgsen, Frode og Myrseth, Inge Bjørn. (2011).
COHIBA user manual - Version 2.3.
NVA
Rapport
Syversveen, Anne Randi; Nilsen, Halvor Møll; Lie, Knut-Andreas; Tveranger, Jan og Abrahamsen, Petter. (2011).
A study on how top surface morphology influences the CO2 storage capacity. CIPR, UIB, Norsk Regnesenteral, SINTEF
NVA
Vitenskapelig foredrag
Abrahamsen, Petter; Fjellvoll, Bjørn; Hauge, Ragnar og Kolbjørnsen, Odd. (2011).
Geostatistics course.
NVA
Faglig foredrag
Kjønsberg, Heidi; Stien, Marita; Fjellvoll, Bjørn; Kolbjørnsen, Odd og Abrahamsen, Petter. (2011).
Methods of the Markov Mesh Multi-Grid Module in RMS.
NVA
Rapport
Abrahamsen, Petter; Almendral-Vazquez, Ariel; Dahle, Pål; Georgsen, Frode og Myrseth, Inge. (2011).
Cohiba user manual version 3.0.
NVA
Rapport
Røe, Per; Abrahamsen, Petter; Georgsen, Frode; Syversveen, Anne Randi og Lia, Oddvar. (2010).
SPE 134912 - Flexible Simulation of Faults.
NVA
Vitenskapelig foredrag
Almendral-Vazquez, Ariel; Dahle, Pål; Abrahamsen, Petter; Skorstad, Arne; Georgsen, Frode og Myrseth, Inge. (2010).
COHIBA user manual — Version 2.1.
NVA
Rapport
Abrahamsen, Petter; Dahle, Pål; Georgsen, Frode og Skorstad, Arne. (2010).
A Consistent Geostatistical Approach for Constraining Multiple Surfaces to Horizontal Wells.
NVA
poster
Abrahamsen, Petter. (2010).
Statistics in the petroleum industry. Norsk statistisk forening
NVA
Vitenskapelig foredrag
Almendral-Vazquez, Ariel; Dahle, Pål; Abrahamsen, Petter; Skorstad, Arne; Georgsen, Frode og Myrseth, Inge. (2010).
COHIBA user manual - Version 2.0.
NVA
Rapport
Almendral-Vazquez, Ariel; Dahle, Pål; Abrahamsen, Petter; Skorstad, Arne; Georgsen, Frode og Myrseth, Inge. (2010).
COHIBA user manual — Version 2.2.
NVA
Rapport
Røe, Per; Abrahamsen, Petter; Georgsen, Frode; Syversveen, Anne Randi og Lia, Oddvar. (2010).
Flexible Simulation of Faults.
NVA
Vitenskapelig Kapittel/Artikkel/Konferanseartikkel
Vis sammendrag
Fault geometry is modelled on basis of seismic data, but restricted by fault observations in wells. Due to uncertainties in depth migration, seismic interpretation and well data, there is a significant uncertainty in the geometry and position of the faults. Fault uncertainty impact reservoir volume, flow properties and well planning, and can be studied by stochastic simulation of faults.
We have developed a method for stochastic simulation of fault surfaces and fault networks using standard geostatistical methods. This is made possible by the fault parameterization used, where the faults are modelled as tilted surfaces. This new method is more flexible and efficient compared to already existing algorithms due to a simpler parameterization. Conditioning to fault observations in wells is also made simpler.
The fault is defined as a two-dimensional surface on a tilted reference plane. The uncertainty for a fault surface is bounded by a volume enclosing the fault surface. The smoothness of the simulated fault surfaces is controlled by variograms. The simulation is done by adding a simulated Gaussian residual. Well conditioning is done by kriging.
Using the described method we can simulate a set of fault realizations where the simulated faults look realistic, are within the defined uncertainty volumes, and honour well observations.
Technical contributions compared to previous work include efficient simulation of fault geometry, a flexible uncertainty model and well conditioning with no performance impact.
Kjønsberg, Heidi; Fjellvoll, Bjørn; Abrahamsen, Petter; Kolbjørnsen, Odd og Stien, Marita. (2009).
Methods of the Multipoint Module in RMS.
NVA
Rapport