EP1606727A2 - Methode pour former rapidement un modele stochastique representatif de la distribution d'une grandeur physique dans un milieu heterogene par une selection appropriee de realisations geostatistiques - Google Patents
Methode pour former rapidement un modele stochastique representatif de la distribution d'une grandeur physique dans un milieu heterogene par une selection appropriee de realisations geostatistiquesInfo
- Publication number
- EP1606727A2 EP1606727A2 EP04720900A EP04720900A EP1606727A2 EP 1606727 A2 EP1606727 A2 EP 1606727A2 EP 04720900 A EP04720900 A EP 04720900A EP 04720900 A EP04720900 A EP 04720900A EP 1606727 A2 EP1606727 A2 EP 1606727A2
- Authority
- EP
- European Patent Office
- Prior art keywords
- realizations
- realization
- geostatistical
- objective function
- initial
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Withdrawn
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/17—Function evaluation by approximation methods, e.g. inter- or extrapolation, smoothing, least mean square method
Definitions
- the present invention relates to a method for rapidly forming a stochastic model representative of the distribution of a physical quantity such as permeability for example, in a porous heterogeneous medium, which is calibrated with respect to dynamic data, by an appropriate selection of realizations geostatistics combined linearly.
- Optimization in a stochastic context consists in determining realizations of a stochastic model which satisfy a set of data observed in the field.
- the realizations to be identified correspond to representations, in the reservoir field, of the distribution of transport properties such as permeability or porosity.
- These achievements form digital reservoir models.
- the available data are, for example, punctual measurements of permeability or porosity, a model of spatial variability determined according to punctual measurements or data directly related to the flows of fluids in an underground reservoir, i.e. pressures, breakthrough time, flow rates, etc. These are often not linearly related to the physical properties to be modeled.
- An achievement drawn at random is generally not in line with all of the data collected. Consistency with the data is ensured in the model by means of an inverse procedure.
- Integrated reservoir engineering studies have two main objectives:
- the reservoir engineer seeks to quantify the uncertainties linked to production forecasts
- the reservoir engineer wants to be able to test different production scenarios to carry out risk studies.
- a classical approach concerning point [3] consists in decomposing into eigenvalues and vectors. The various eigenvalues obtained then make it possible to find a compromise between the uncertainty obtained on the parameters at the end of calibration and the number of parameters which can be estimated from the available data.
- any geostatistical realization always contributes, even minimal, to the fall of. the objective function (J). Consequently, a number of optimal geostatistical realizations are linearly combined by the gradual deformation method. These optimal realizations are themselves derived from a linear combination of initial geostatistical realizations whose combination coefficients are chosen so as to propose a direction of search for gradual deformations as close as possible to the direction of descent given by the gradients.
- This approach was the subject of the patent application 02 / 13.632 of the applicant.
- the method according to the invention makes it possible to form a stochastic digital model of the Gaussian or related type, giving an image of the distribution of a physical quantity in a porous heterogeneous medium, which is calibrated with respect to data obtained by measurements carried out in the medium or previous observations, and characteristics of the movement of fluids in the medium.
- It comprises an iterative process of gradual deformation where one linearly combines with each iteration, an initial geostatistical realization (y) of at least part of the medium, and a number (Nl) (N> 1) other realizations independent of the initial implementation by imposing constraints on the coefficients of the linear combination, and an objective function is minimized measuring the difference between a set of non-linear data deduced from the said combination by means of a simulator, and the said dynamic data, the iterative process being repeated until an optimal realization of the stochastic model is obtained.
- the ( ⁇ -l) other realizations are selected from the (N-l) indicators of highest absolute value.
- the N realizations are selected from the N indicators of highest absolute value.
- FIG. 2 is a geometric representation of the method for finding the best initialization point for the optimization algorithm in the case of refinement indicators for gradual deformations;
- the normality constraint is automatically checked when working in spherical coordinates ⁇ 1 , ..., ⁇ N _ 1 ⁇ .
- the new realization z is therefore a function of (N-
- refinement indicators has been applied to parametrization by gradual deformations.
- a number N generally small
- realizations z ( . E R " m are chosen at random, or nm corresponds to the number of geostatistical meshes (generally large).
- the use of refinement indicators will allow l user to reduce the number of randomly selected geostatistical realizations to one or even zero.
- the user chooses the (Nl) realizations z 2 —z N used in the gradual deformations from a set of N # (N # "N) realizations z 2 —Z N " .
- the idea is to generate the realizations z 2 ... z N , from a large number of random seeds and to take into account for the gradual deformation only the ( ⁇ -l) realizations having the strongest indicators of refinement ⁇ . , which we define now.
- Let p [p v ..., p,), and consider the following constraint optimization problem
- L is the Lagrangian defined by:
- the geostatistical gradient dj / dz [z "je R nm corresponds to the derivative of the objective function J with respect to each geostatistical cell of realization z * .
- the minimum (optimal) value of the objective function associated with the second member b is therefore:
- a well-known constraint optimization result tells us that the Lagrange multiplier ⁇ * coincides with the derivative of the optimal objective function J b * with respect to the i-th element b i of the second member of the constraint:
- the i-th component ⁇ l of the Lagrange multiplier ⁇ therefore indicates the sensitivity of the optimal objective function J b * when we take into account the i-th degree of freedom, that is to say that we uses the i-th realizations z t for the parametrization of the gradual deformations.
- Equation 10 Equation 10 can then be rewritten as:
- the user In order to select the N realizations used in the gradual deformations, the user generates as in case 1 a large number N # of geostatistical realizations and calculates the initialization indicators for the gradual deformations:
- important can potentially significantly decrease the objective function for a correct sign ⁇ p ⁇ .
- the user sorts the initialization indicators in decreasing order of absolute value and chooses for the gradual deformation the N realizations having the highest absolute value.
- the preliminary step to the calculation of the refinement indicators [Eq. (6)] consists in calculating the geostatistical gradient dJ / dz. To this end, let us first consider the different stages of the direct problem when the gradual deformations are used as parametrization of the geological model (Fig. 1).
- the four successive stages are:
- Geological modeling case of lognormal distributions or facies models. The conditioning to the static well data is carried out.
- One of the essential points of the proposed methodology is to calculate these gradients by the adjunct state method.
- the computation of the gradient dJ / dK is done by a discrete assistant state.
- the second term can also be calculated by assistant state if necessary.
- the third term corresponds to the derivation of the geological modeling step and can be easily calculated analytically.
- Equation (9) tells us that the sign of the refinement indicators contains important information. Suppose that a given indicator has a positive sign. If a positive weight is attached to the associated realization, this will tend to decrease the objective function (first order). The same analysis holds for negative indicators. The user will therefore have every interest in initializing the optimization algorithm with ⁇ giving linear combination coefficients of the same sign as the indicator under consideration.
- the user determines the (Nl) realizations z 2 —Z N used for the gradual deformations based on the associated refinement indicators.
- the user calculated V ⁇ 7 (z 1 ) and, by simple scalar product, the components ⁇ x ... ⁇ N of V ((l, 0 ... ⁇ )). So he can search on the sphere
- Facial models correspond to models with discontinuities at the level of physical quantities such as permeability for example, which makes the term [3] of equation (14) non-derivable.
- the only petrophysical property considered is permeability.
- the permeability is modeled by a lognormal distribution with an average equal to 100 mD and a variance equal to (lO ⁇ ) 2 mD 2 .
- the porosity is constant in the tank.
- the only data from the flow simulator are the well pressures. Five wells are crossed by the reservoir: a producer well in the center of the model and four observer wells arranged in a cross around the producer well.
- a realization generated from a random seed serves as a reference model.
- a fluid flow simulation is conducted on this model, which gives us reference well pressures.
- the objective function is formulated in the least sense square. We do not consider a step of change of scale. The simulation is directly conducted on the model considered.
- loop 2 corresponds to the optimization carried out with the realization z x and the realizations having the refinement indicators of highest absolute value in the game considered.
- - loop 4 corresponds to the optimization carried out with realization z and the realizations having the refinement indicators of lowest absolute value in the game considered.
- loop 1 corresponds to the evolution of the objective function J for an optimization carried out with the geostatistical realization z x and two other realizations chosen at random.
- loop 2 corresponds to the optimization carried out with realization z x and the realizations having the initialization indicators of highest absolute value in the game considered.
- loop 4 corresponds to the optimization carried out with realization z x and the realizations having the initialization indicators of lowest absolute value in the game considered.
Landscapes
- Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Computational Mathematics (AREA)
- Data Mining & Analysis (AREA)
- Mathematical Physics (AREA)
- Theoretical Computer Science (AREA)
- Algebra (AREA)
- Databases & Information Systems (AREA)
- Software Systems (AREA)
- General Engineering & Computer Science (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
Description
Claims
Applications Claiming Priority (3)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
FR0303276 | 2003-03-18 | ||
FR0303276A FR2852710B1 (fr) | 2003-03-18 | 2003-03-18 | Methode pour former rapidement un modele stochastique representatif de la distribution d'une grandeur physique dans un milieu heterogene par une selection appropriee de realisations geostatistiques |
PCT/FR2004/000644 WO2004086280A2 (fr) | 2003-03-18 | 2004-03-16 | Methode pour former rapidement un modele stochastique representatif de la distribution d’une grandeur physique dans un milieu heterogene par une selection appropriee de realisations geostatistiques |
Publications (1)
Publication Number | Publication Date |
---|---|
EP1606727A2 true EP1606727A2 (fr) | 2005-12-21 |
Family
ID=32922242
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
EP04720900A Withdrawn EP1606727A2 (fr) | 2003-03-18 | 2004-03-16 | Methode pour former rapidement un modele stochastique representatif de la distribution d'une grandeur physique dans un milieu heterogene par une selection appropriee de realisations geostatistiques |
Country Status (6)
Country | Link |
---|---|
US (1) | US7558715B2 (fr) |
EP (1) | EP1606727A2 (fr) |
CA (1) | CA2519184C (fr) |
FR (1) | FR2852710B1 (fr) |
NO (1) | NO20054259L (fr) |
WO (1) | WO2004086280A2 (fr) |
Families Citing this family (17)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
FR2869116B1 (fr) * | 2004-04-14 | 2006-06-09 | Inst Francais Du Petrole | Methode pour construire un modele geomecanique d'une zone souterraine destine a etre couple a un modele de reservoir |
FR2869421B1 (fr) * | 2004-04-27 | 2006-06-02 | Inst Francais Du Petrole | Methode de reconstruction d'un modele stochastique, representatif d'un milieu heterogene poreux, pour ameliorer son calage par les donnees de production |
US7805248B2 (en) * | 2007-04-19 | 2010-09-28 | Baker Hughes Incorporated | System and method for water breakthrough detection and intervention in a production well |
FR2919932B1 (fr) * | 2007-08-06 | 2009-12-04 | Inst Francais Du Petrole | Methode pour evaluer un schema de production d'un gissement souterrain en tenant compte des incertitudes |
WO2009145960A1 (fr) | 2008-04-17 | 2009-12-03 | Exxonmobil Upstream Research Company | Outil de support de decision basee sur une optimisation robuste, utilise dans la planification de developpement de reservoir |
EP2291761A4 (fr) * | 2008-04-18 | 2013-01-16 | Exxonmobil Upstream Res Co | Outil d'aide à la décision à base de processus de décision de markov pour une planification de développement de réservoir |
BRPI0910333A2 (pt) | 2008-04-21 | 2015-10-06 | Exxonmobil Upstream Res Co | métodos para planejamento de desenvolvimento de um reservatório, para suporte à decisão que considera o desenvolvimento de recursos de petróleo, para otimização do planejamento de desenvolvimento com base em computador para um reservatório de hidrocarboneto, e para produzir hidrocarbonetos, e, produto de programa de computador |
AU2009341851B2 (en) | 2009-03-11 | 2015-07-16 | Exxonmobil Upstream Research Company | Gradient-based workflows for conditioning of process-based geologic models |
AU2009341852B2 (en) | 2009-03-11 | 2015-08-20 | Exxonmobil Upstream Research Company | Adjoint-based conditioning of process-based geologic models |
EP2499567A4 (fr) | 2009-11-12 | 2017-09-06 | Exxonmobil Upstream Research Company | Procédé et appareil de modélisation et de simulation de réservoirs |
FR2953039B1 (fr) * | 2009-11-26 | 2012-01-13 | Inst Francais Du Petrole | Methode d'exploitation d'un gisement petrolier par reconstruction de modele de reservoir |
WO2012021292A1 (fr) | 2010-08-09 | 2012-02-16 | Conocophillips Company | Procédé de mise à l'échelle supérieure de réservoir avec une transmissibilité préservée |
BR112013006777B1 (pt) * | 2010-09-27 | 2021-10-26 | Total Sa | Método de simulação de fenômenos de carstificação em uma região cárstica e dispositivo de simulação de fenômenos de carstificação em uma região cárstica |
US8942966B2 (en) * | 2010-10-20 | 2015-01-27 | Conocophillips Company | Method for parameterizing and morphing stochastic reservoir models |
US9488047B2 (en) | 2011-04-04 | 2016-11-08 | Conocophillips Company | Reservoir calibration parameterization method |
CA2887319C (fr) * | 2012-10-05 | 2019-09-17 | Total Sa | Procede pour determiner une region karstique |
FR3004270B1 (fr) | 2013-04-05 | 2015-05-01 | Storengy | Methode de determination d'un modele cale pour un reservoir souterrain de fluide |
Family Cites Families (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US5838634A (en) * | 1996-04-04 | 1998-11-17 | Exxon Production Research Company | Method of generating 3-D geologic models incorporating geologic and geophysical constraints |
US6549879B1 (en) * | 1999-09-21 | 2003-04-15 | Mobil Oil Corporation | Determining optimal well locations from a 3D reservoir model |
US6480790B1 (en) * | 1999-10-29 | 2002-11-12 | Exxonmobil Upstream Research Company | Process for constructing three-dimensional geologic models having adjustable geologic interfaces |
FR2821946B1 (fr) * | 2001-03-07 | 2003-05-16 | Inst Francais Du Petrole | Methode pour deformer graduellement une repartition intiale d'objets dans un milieu heterogene, generee par simulation d'un modele stochastique de type objet, pour l'adapter au mieux a des contraintes physiques imposees |
FR2823877B1 (fr) * | 2001-04-19 | 2004-12-24 | Inst Francais Du Petrole | Methode pour contraindre par des donnees dynamiques de production un modele fin representatif de la repartition dans le gisement d'une grandeur physique caracteristique de la structure du sous-sol |
-
2003
- 2003-03-18 FR FR0303276A patent/FR2852710B1/fr not_active Expired - Fee Related
-
2004
- 2004-03-16 EP EP04720900A patent/EP1606727A2/fr not_active Withdrawn
- 2004-03-16 US US10/549,193 patent/US7558715B2/en not_active Expired - Fee Related
- 2004-03-16 CA CA2519184A patent/CA2519184C/fr not_active Expired - Fee Related
- 2004-03-16 WO PCT/FR2004/000644 patent/WO2004086280A2/fr active Application Filing
-
2005
- 2005-09-15 NO NO20054259A patent/NO20054259L/no not_active Application Discontinuation
Non-Patent Citations (1)
Title |
---|
See references of WO2004086280A2 * |
Also Published As
Publication number | Publication date |
---|---|
WO2004086280A2 (fr) | 2004-10-07 |
WO2004086280A3 (fr) | 2004-10-28 |
US7558715B2 (en) | 2009-07-07 |
CA2519184C (fr) | 2013-05-14 |
CA2519184A1 (fr) | 2004-10-07 |
FR2852710B1 (fr) | 2005-04-29 |
NO20054259D0 (no) | 2005-09-15 |
FR2852710A1 (fr) | 2004-09-24 |
NO20054259L (no) | 2005-12-16 |
US20060241925A1 (en) | 2006-10-26 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
EP1606727A2 (fr) | Methode pour former rapidement un modele stochastique representatif de la distribution d'une grandeur physique dans un milieu heterogene par une selection appropriee de realisations geostatistiques | |
EP1760492B1 (fr) | Méthode pour mettre à jour un modèle géologique de réservoir a l'aide de données dynamiques | |
EP2406750B1 (fr) | Conditionnement par modèle adjoint de modèles géologiques à base de processus | |
Schwenk et al. | The life of a meander bend: Connecting shape and dynamics via analysis of a numerical model | |
EP2680045B1 (fr) | Procédé d'exploitation d'un reservoir geologique à partir d'un modèle de réservoir calé au moyen d'un parametrage multi-echelles | |
Cumming et al. | Multiwell deconvolution | |
EP2400320B1 (fr) | Procédé d'exploitation d'un gisement pétrolier à partir d'un modèle de réservoir déformé graduellement au moyen de cosimulations | |
Wang et al. | A hybrid framework for reservoir characterization using fuzzy ranking and an artificial neural network | |
CN106324674B (zh) | 一种页岩气toc叠前地震反演预测方法 | |
CA2821099C (fr) | Procede d'exploitation d'un reservoir geologique a partir d'un modele de reservoir cale par le calcul d'une loi analytique de distribution conditionnelle de parametres incertains du modele | |
Hegstad et al. | Uncertainty in production forecasts based on well observations, seismic data, and production history | |
Abadpour et al. | Integrated geo-modeling and ensemble history matching of complex fractured carbonate and deep offshore turbidite fields, generation of several geologically coherent solutions using ensemble methods | |
Rwechungura et al. | Application of particle swarm optimization for parameter estimation integrating production and time lapse seismic data | |
EP2770162B1 (fr) | Procédé d'exploitation d'un réservoir géologique au moyen d'un modèle de réservoir calé et cohérent vis à vis des propriétés d'écoulement | |
Shokir | A novel model for permeability prediction in uncored wells | |
Sahni et al. | Generating multiple history-matched reservoir model realizations using wavelets | |
Momeneh et al. | Forecasting of groundwater level fluctuations using a hybrid of multi-discrete wavelet transforms with artificial intelligence models | |
Pan et al. | Efficient subsurface modeling with sequential patch generative adversarial neural networks | |
Johnson et al. | Review of geodetic and geologic deformation models for 2023 US National Seismic Hazard Model | |
Landa et al. | Sensitivity Analysis of Petrophysical Properties Spatial Distributions, and Flow Performance Forecasts to Geostatistical Parameters Using Derivative Coefficients | |
Huguet et al. | Automated History-Matching of Radial Models Using Self Organizing Classification Method for Underground Gas Storage Reservoirs Characterization | |
Yadavalli et al. | Use of pressure transient data to estimate permeability variograms | |
Kaufman et al. | Probabilistic Aggregation of Uncertain Geological Resources | |
CN117610429A (zh) | 基于深度学习的测井曲线补全模型训练方法及装置 | |
Cao et al. | A critical reflection of computational fluid dynamics applications to fluvial sedimentary systems |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
PUAI | Public reference made under article 153(3) epc to a published international application that has entered the european phase |
Free format text: ORIGINAL CODE: 0009012 |
|
17P | Request for examination filed |
Effective date: 20051018 |
|
AK | Designated contracting states |
Kind code of ref document: A2 Designated state(s): AT BE BG CH CY CZ DE DK EE ES FI FR GB GR HU IE IT LI LU MC NL PL PT RO SE SI SK TR |
|
AX | Request for extension of the european patent |
Extension state: AL LT LV MK |
|
DAX | Request for extension of the european patent (deleted) | ||
RBV | Designated contracting states (corrected) |
Designated state(s): GB NL |
|
REG | Reference to a national code |
Ref country code: DE Ref legal event code: 8566 |
|
RIN1 | Information on inventor provided before grant (corrected) |
Inventor name: MEZGHANI, MOKHLES Inventor name: CHAVENT, GUY Inventor name: SCHAAF, THOMAS |
|
STAA | Information on the status of an ep patent application or granted ep patent |
Free format text: STATUS: THE APPLICATION IS DEEMED TO BE WITHDRAWN |
|
18D | Application deemed to be withdrawn |
Effective date: 20141001 |