EP2022934A2 - Methode zur Evaluierung eines Produktionsschemas von unterirdischen Quellvorkommen unter Berücksichtigung von Unsicherheitsfaktoren - Google Patents

Methode zur Evaluierung eines Produktionsschemas von unterirdischen Quellvorkommen unter Berücksichtigung von Unsicherheitsfaktoren Download PDF

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EP2022934A2
EP2022934A2 EP08290725A EP08290725A EP2022934A2 EP 2022934 A2 EP2022934 A2 EP 2022934A2 EP 08290725 A EP08290725 A EP 08290725A EP 08290725 A EP08290725 A EP 08290725A EP 2022934 A2 EP2022934 A2 EP 2022934A2
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Prior art keywords
responses
model
deposit
simulator
production
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French (fr)
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EP2022934A3 (de
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Daniel Busby
Mathieu Feraille
Thomas Romary
Samir Touzani
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IFP Energies Nouvelles IFPEN
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IFP Energies Nouvelles IFPEN
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    • E—FIXED CONSTRUCTIONS
    • E21—EARTH OR ROCK DRILLING; MINING
    • E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B43/00—Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials or a slurry of minerals from wells

Definitions

  • the present invention relates to the field of exploration and exploitation of oil deposits. More particularly, the invention relates to the evaluation of such deposits, by studying and optimizing production patterns of such oil deposits.
  • a production scheme is an option for developing a deposit. It groups all the parameters necessary for the production of a deposit. These parameters can be the position of a well, the level of completion, the drilling technique ...
  • the study of a deposit has two main phases: a reservoir characterization phase and a production forecasting phase.
  • the characterization phase of the reservoir consists of constructing a reservoir model.
  • a reservoir model is a model describing the spatial structure of the deposit, in the form of a discretization of space. This discretization is materialized by a set of meshes. At each of these meshes, we associate values of properties characterizing the deposit: porosity, permeability, lithology, pressure, nature of the fluids, ...
  • the engineers have access only to a small part of the deposit they study ( measurements on cores, logs, well tests, ). They need to extrapolate these point data across the entire oil field to build a reliable reservoir model. Consequently, the notion of uncertainty must be constantly taken into account.
  • a flow simulator is a software allowing, among other things, to model the production of a deposit as a function of time, from measurements describing the deposit, that is to say, from the reservoir model.
  • a flow simulator works by accepting input parameters, and solving physical fluid mechanics equations in porous media, to deliver information called responses.
  • the set of input parameters is contained in the reservoir model.
  • the properties associated with the meshes of this model are then called settings. These parameters are associated with the geology of the deposit, the petro-physical properties, the development of the deposit and the numerical options of the simulator.
  • the responses (outputs) provided by the simulator are, for example, the production of oil, water or gas tank and each well for different times.
  • the flow simulator returns a single value for each response (output). The flow simulator is then qualified as deterministic.
  • the majority of input parameters are uncertain. These uncertainties result in the fact that one can not assign a single value, which is sure of value, to a parameter of the reservoir model. For example, we can not ensure that the porosity at one point of the deposit is 20%. It can best be considered that the porosity is between 15% and 25% at this point. This is because the input parameters are determined using a limited number of measurements and information. The possible responses of the flow simulator are therefore multiple, given the inherent uncertainty of the reservoir model. In our example, there will be a response from the simulator if the porosity is 15%, a different response if the porosity is 20.5% ... It is thus essential to be able to quantify the uncertainty on the outputs of the simulator. Similarly, a correct characterization of the uncertainty of the input parameters is essential. It is also important to determine input parameters that have a significant effect on interest responses.
  • any response surface makes a more or less important prediction error, depending on the response it tries to approximate.
  • the addition of information i.e. simulations allows the construction of an increasingly predictive response surface.
  • the object of the invention is an alternative method for evaluating underground deposit production patterns by estimating the production of such deposits using an approximate model, and iteratively adjusted to reproduce at better simulator responses, while controlling the number of simulations required for its construction.
  • the input parameters may be uncertain, that is, the values of these input parameters are uncertain.
  • the deposit responses predicted by the approximate analytical model, can be analyzed by quantifying an influence of each of the input parameters on each of the responses, using an overall sensitivity analysis, in which sensitivity using the analytical model.
  • an overall sensitivity analysis in which sensitivity using the analytical model.
  • the input parameters comprise at least one stochastic field
  • this stochastic field it is possible to decompose this stochastic field into a number n of components via a Karhunen-Loeve decomposition.
  • the components of the stochastic field that have an impact on the responses are then selected using the global sensitivity analysis.
  • Any flow simulator makes it possible to calculate the production of hydrocarbons or water as a function of time, based on physical parameters characteristic of the oil reservoir, such as the number of layers of the reservoir, the permeability of the layers, the force of the the aquifer, the position of the oil wells, etc.
  • the physical parameters characteristic of the oil field it is preferable to select input parameters having an influence on the profiles of production of hydrocarbons or water by the deposit.
  • the selection of the parameters can be done either with respect to the physical knowledge of the oil field, or by a sensitivity study. For example, it is possible to implement a Student or Fischer statistical test.
  • Parameters may be intrinsic to the oil reservoir. For example, the following parameters may be considered: permeability of certain layers of the reservoir, aquifer strength, residual oil saturation after sweeping with water ...
  • Parameters may correspond to deposit development options. These parameters can be the position of a well, the level of completion, the drilling technique.
  • the uncertainties associated with these parameters are characterized. For example, a value of a parameter can be replaced by a variation interval of this parameter.
  • Step 2 Construction of an approximate analytical model of the simulator
  • This approximate model reflects the behavior of given responses, for example the cumulative oil produced at 10 years, according to some input parameters.
  • a plan indicates different sets of values for the uncertain parameters.
  • Each set of uncertain parameter values is used to perform a flow simulation.
  • each simulation represents a point.
  • Each point corresponds to values for the uncertain parameters and therefore to a possible reservoir model.
  • the choice of these points can involve many types of criteria, such as orthogonality or space-filling.
  • first or second order polynomials neural networks, vector support machines or possibly higher order polynomials than two .
  • Numerous other techniques are known to those skilled in the art, such as wavelet, SVM, self reproducing Hilbert methods, or non-parametric regression based on a Gaussian or kriging process ( Kennedy M., O'Hagan A .: “Bayesian calibration of computer models (with discussion)”. J. Statist. Soc. Ser. B Stat. METHODOL. 68, 425-464, 2001 ).
  • the choice of the method depends on the one hand on the number of simulations that can be envisaged by the user, and on the other hand, on the initial experimental design used.
  • the method comprises a measurement of the prediction accuracy of this model so as to define an evaluation criterion associated with the precision of the constructed approximate model.
  • the figure 2 illustrates an example of the evolution of the estimated prediction error ( Err ) by a response surface (approximate model), as a function of the number of simulations ( Nsim ) used to construct the response surface.
  • the response surface approximates the output of the flow simulator corresponding to the oil flow of the tank after 10 years of production.
  • This criterion allows a user to decide whether to add simulations to improve the predictive reliability of the model.
  • the number p of simulations carried out at each iteration can be controlled by the user, depending on the number of machines available to perform simulations for example.
  • step e) The addition of simulations in step e) is repeated, automatically, to satisfy a stopping criterion which is related to the degree of prediction desired by the user, defined in step a), by example average prediction of 5% of the response studied.
  • a stopping criterion which is related to the degree of prediction desired by the user, defined in step a)
  • An example of estimation of the prediction is obtained from the average of the cross-validation errors in each zone.
  • the principle of optimization of the production scheme consists of defining different production scenarios, and for each of them, predicting production. This technique also makes it possible, in the same way, to economically evaluate a petroleum deposit.
  • the approximate model is used because it is simple and analytical and, therefore, every estimate obtained by this model is immediate. This saves a lot of time.
  • the use of this model allows the reservoir engineer to test as many scenarios as he wants, without worrying about the time required to perform a numerical flow simulation, and above all it allows him to take into account the uncertainties by testing different values of input parameters.
  • the approximate analytical model is used with Monte Carlo or Quasi Monte Carlo direct sampling techniques (MCMC, Hypercube Latin, 3) in order to propagate the uncertainties of the input parameters on the selected simulator response (s).
  • MCMC Monte Carlo or Quasi Monte Carlo direct sampling techniques
  • the approximate model is used to perform an overall sensitivity analysis, so as to select the parameters influencing the production of the deposit, in order to carry out the measurements necessary for a better evaluation of the deposit.
  • f 0 ⁇ ⁇ p ⁇ f x ⁇ dx and if ( he , ..., is ) ⁇ ( j1 , ..., jl ), then f ⁇ p ⁇ f i ⁇ 1 , ... , isf j ⁇ 1 , ... , jl ⁇ dx
  • S i is called the first order sensitivity index for the factor x i . This index measures the part of the variance of the response explained by the effect of x i .
  • S i, j for i ⁇ j, is called the second order sensitivity index. This index measures the proportion of response variance due to interactions between the effects of x i and x j .
  • the total sensitivity index, S Ti for a particular parameter x i can also be very useful for measure the part of the variance of the response explained by all the effects in which x i plays a role.
  • the global sensitivity analysis makes it possible to explain the variability of the responses as a function of the input parameters, through the definition of total or partial sensitivity indices. These indices can be estimated by Monte Carlo or Quasi Monte Carlo techniques to approximate the different multidimensional integrals, requiring a large sampling.
  • the overall sensitivity analysis can not be used directly using a flow simulator.
  • the sensitivity index calculations are performed using analytical models for each response. These analytical models are constructed as previously described.
  • the Global Sensitivity Analysis (ASG) used in the invention does not have the usual limitations related to the hypotheses that other methods can be used that allow the calculation of standard sensitivity indices Spearman, Pearson, SRC, rank index, ...
  • the only hypothesis is that the uncertain parameters are independent, which greatly expands the use of ASG using Sobol decomposition. This assumption is generally respected in reservoir engineering problems, since the links between parameters are known a priori.
  • the Global Sensitivity Analysis (ASG) of the uncertain parameters on the simulator responses also makes it possible to evaluate the average effect of a parameter on a given response.
  • This average effect can be used for example for controllable parameters, eg position a well, injection flow etc ... and is therefore a simple tool of behavior parameters.
  • the use of the approximate model to make the ASG allows to determine the influential parameters, and how they are influential. It is thus possible to know the total impact of a parameter, as well as its combined impact with one or more other parameters on the production or economic response of the deposit.
  • the ASG clearly allows a better understanding of the deposit's behavior.
  • the determination of the average effects of the parameters is also a tool to characterize the average influence of a parameter, given the uncertainty of the other parameters on the responses in production or economic reservoir.
  • the input parameters comprise stochastic fields, eg permeability, porosity, facies, etc.
  • stochastic fields eg permeability, porosity, facies, etc.
  • the uncertainty coming from the geostatistical maps is often neglected in the methods of uncertainty analysis based on plans. experience.
  • the stochastic field is decomposed into a number n of components via the Karhunen-Loeve decomposition (M. Loève Probability Theory, Princeton University Press, 1955).
  • the geostatistical techniques used in reservoir engineering to model the permeability and porosity quantities of rocks are mostly based on random Gaussian functions, discretized on a mesh covering the physical space of the reservoir.
  • the Karhunen-Loève decomposition of a geostatistical model consists of representing it in the base formed of the eigenvectors of its covariance operator. This gives a functional representation of the random field.
  • the method according to the invention is a tool for the analysis of the uncertainties of a flow simulator, and to help an engineer to reduce this uncertainty, focusing on the characterization of the parameters whose uncertainty contributes mainly to the poor characterization of the outputs.
  • This method provides a robust and cost-effective tool (in terms of the number of simulations) for the global sensitivity analysis and the propagation of uncertainties. It allows the engineer to control the degree of approximation of his results by analyzing in real time the advantages in terms of prediction compared to the number of simulations carried out.
  • the method allows the uncertainties of the geostatistical model (permeability, porosity, facies, etc.) to be taken into account by using surface response techniques and global sensitivity analysis.

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EP08290725A 2007-08-06 2008-07-25 Methode zur Evaluierung eines Produktionsschemas von unterirdischen Quellvorkommen unter Berücksichtigung von Unsicherheitsfaktoren Ceased EP2022934A3 (de)

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FR0705740A FR2919932B1 (fr) 2007-08-06 2007-08-06 Methode pour evaluer un schema de production d'un gissement souterrain en tenant compte des incertitudes

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CN107018672A (zh) * 2014-12-03 2017-08-04 贝克休斯公司 能源行业作业特征化和/或优化
EP3227530A4 (de) * 2014-12-03 2018-08-08 Baker Hughes Incorporated Energiebranchenoperationscharakterisierung und/oder -optimierung
CN116305593A (zh) * 2023-05-23 2023-06-23 西安交通大学 一种具有强可移植性的全局敏度分析方法

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US8392164B2 (en) 2013-03-05
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CA2638227C (fr) 2016-09-27
US20090043555A1 (en) 2009-02-12
CA2638227A1 (fr) 2009-02-06

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